1. Equations & Inequalities

Linear Inequalities

1. Equations & Inequalities

Linear Inequalities

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Linear Inequalities with Fractions & Variables on Both Sides

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Using Interval Notation to Express Inequalities - Example 1

Using Interval Notation to Express Inequalities - Example 2

Interval Notation - A basic question!

Writing Compound Inequalities Using Interval Notation - Example 2

Drawing a Number Line to Match an Inequality

Union and intersection of intervals

Finding the union and intersections of intervals examples

Definition and Technique For Solving Linear Inequalities

Solving Two - Step Linear Inequalities

Solving 3 Basic Linear Inequalities

Solving Basic Linear Inequalities Involving Multiplication or Division

An Introduction To Solving Linear Inequalities - Example 1

An Introduction To Solving Linear Inequalities - Example 2

An Introduction To Solving Linear Inequalities - Example 3

Solving Word Problems Involving Inequalities - Example 2

Solving Word Problems Involving Inequalities - Example 3

Solving Inequalities with No Solution or Infinite Solutions

Solving inequalities with no solution or all real numbers as solutions

Pine View Middle School Math

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Solving A Compound Linear Inequality

Absolute Value Inequalities - How to Solve

Mario's Math Tutoring

Solving Absolute Value Inequalities, MORE Examples - Example 2

Solving Linear Absolute Value Equations and Inequalities

Solving Absolute Value Inequalities - Example 1

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Multiple Choice

Express the given set in interval notation and graph.

{ $x$ | 14 ≤ $x$ < 26}

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Multiple Choice

Express the given interval in set builder notation and graph. (−∞, 0]

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Multiple Choice

Express the given set in interval notation and graph.

${$ $x$ $∣$ $x is less than or equal to 7$ $}$

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Multiple Choice

Solve the inequality. Express the solution set in interval notation and graph. $2x+12>19$

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Multiple Choice

Solve the inequality. Express the solution set in interval notation and graph.

$\frac13\left(x+1\right)\ge\frac15\left(3+2x\right)$

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Textbook Question

Match each equation or inequality in Column I with the graph of its solution set in Column II. | x | = 7

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Textbook Question

Match the inequality in each exercise in Column I with its equiva-lent interval notation in Column II. x<-6

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Textbook Question

In Exercises 1–14, express each interval in set-builder notation and graph the interval on a number line. (1, 6]

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Textbook Question

Match each equation or inequality in Column I with the graph of its solution set in Column II. | x | = -7

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Textbook Question

Match the inequality in each exercise in Column I with its equiva-lent interval notation in Column II. x≤6

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Textbook Question

Match the inequality in each exercise in Column I with its equiva-lent interval notation in Column II. -2

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Textbook Question

In Exercises 1–14, express each interval in set-builder notation and graph the interval on a number line. [- 5, 2)

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Textbook Question

Match each equation or inequality in Column I with the graph of its solution set in Column II. | x | > -7

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Textbook Question

Match the inequality in each exercise in Column I with its equiva-lent interval notation in Column II. x^2≥0

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Textbook Question

Match each equation or inequality in Column I with the graph of its solution set in Column II. | x | > 7

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Textbook Question

Match the inequality in each exercise in Column I with its equiva-lent interval notation in Column II . x≥-6

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Textbook Question

Match each equation or inequality in Column I with the graph of its solution set in Column II. | x | < 7

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Textbook Question

In Exercises 1–14, express each interval in set-builder notation and graph the interval on a number line. [- 3, 1]

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Textbook Question

Match the inequality in each exercise in Column I with its equiva-lent interval notation in Column II. 6≤x

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Textbook Question

Match each equation or inequality in Column I with the graph of its solution set in Column II. | x | ≥ 7

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Textbook Question

Match each equation or inequality in Column I with the graph of its solution set in Column II. | x | ≤ 7

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Textbook Question

In Exercises 1–14, express each interval in set-builder notation and graph the interval on a number line. (2, ∞)

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Textbook Question

Match each equation or inequality in Column I with the graph of its solution set in Column II. | x | ≠ 7

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Textbook Question

In Exercises 1–14, express each interval in set-builder notation and graph the interval on a number line. [- 3, ∞)

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Textbook Question

In Exercises 1–14, express each interval in set-builder notation and graph the interval on a number line. (- ∞, 3)

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Textbook Question

In Exercises 1–14, express each interval in set-builder notation and graph the interval on a number line. (- ∞, 5.5)

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Textbook Question

In Exercises 15–26, use graphs to find each set. (- 3, 0) ∩ [- 1, 2]

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Textbook Question

In Exercises 15–26, use graphs to find each set. (- 3, 0) ⋃ [- 1, 2]

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Textbook Question

Solve each inequality. Give the solution set in interval notation. See Examples 1 and 2. 3(x+5)+1≥5+3x

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Textbook Question

In Exercises 15–26, use graphs to find each set. (- ∞, 5) ∩ [1, 8)

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Textbook Question

Solve each inequality. Give the solution set in interval notation. See Examples 1 and 2. 8x-3x+2<2(x+7)

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Textbook Question

Solve each inequality. Give the solution set in interval notation. See Examples 1 and 2. 2-4x+5(x-1)<-6(x-2)

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Textbook Question

Solve each inequality. Give the solution set in interval notation. See Examples 1 and 2. (4x+7)/-3≤2x+5

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Textbook Question

In Exercises 15–26, use graphs to find each set. (- ∞, 5) ⋃ [1, 8)

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Textbook Question

Solve each inequality. Give the solution set in interval notation. See Examples 1 and 2. (2x-5)/-8≤1-x

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Textbook Question

Solve each inequality. Give the solution set in interval notation. See Examples 1 and 2. (1/3)x+(2/5)x-(1/2)(x+3)≤1/10

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Textbook Question

In Exercises 15–26, use graphs to find each set. [3, ∞) ∩ (6, ∞)

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Textbook Question

Solve each inequality. Give the solution set in interval notation. See Examples 1 and 2. -(2/3)x-(1/6)x+(2/3)(x+1)≤4/3

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Textbook Question

In Exercises 15–26, use graphs to find each set. [3, ∞) ⋃ (6, ∞)

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Textbook Question

In all exercises, other than exercises with no solution, use interval notation to express solution sets and graph each solution set on a number line. In Exercises 27–50, solve each linear inequality. 5x + 11 < 26

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Textbook Question

Solve each inequality. Give the solution set in interval notation. | 3x - 4 | < 2

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Textbook Question

Solve each inequality. Give the solution set in interval notation. See Example 4. -5<5+2x<11

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Textbook Question

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Textbook Question

Solve each inequality. Give the solution set in interval notation. . | 3x - 4 | ≥ 2

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Textbook Question

Solve each inequality. Give the solution set in interval notation. | 1/2 - x | ≤ 2

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Textbook Question

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Textbook Question

Solve each inequality. Give the solution set in interval notation. See Example 4. 10≤2x+4≤16

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Textbook Question

Solve each inequality. Give the solution set in interval notation. | 3/5 + x | < 1

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Textbook Question

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Textbook Question

Solve each inequality. Give the solution set in interval notation. See Example 4. 2>-6x+3>-3

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Textbook Question

Solve each inequality. Give the solution set in interval notation. 5| x + 1 | > 10

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Textbook Question

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Textbook Question

Solve each inequality. Give the solution set in interval notation. See Example 4. -4≤(x+1)/2≤5

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Textbook Question

Solve each inequality. Give the solution set in interval notation. | 5 - 3x | > 7

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Textbook Question

Solve each inequality. Give the solution set in interval notation. | 7 - 3x | > 4

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Textbook Question

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Textbook Question

Solve each inequality. Give the solution set in interval notation. | 5 - 3x | ≤ 7

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Textbook Question

Solve each inequality. Give the solution set in interval notation. See Example 4. 1≤(4x-5)/2<9

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Textbook Question

Solve each inequality. Give the solution set in interval notation. | 7 - 3x | ≤ 4

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Textbook Question

Solve each inequality. Give the solution set in interval notation. | (2/3)x + 1/2 | ≤ 1/6

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Textbook Question

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Textbook Question

Solve each inequality. Give the solution set in interval notation. | 5/3 - (1/2) x | > 2/9

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Textbook Question

Solve each inequality. Give the solution set in interval notation. | 0.01x + 1 | < 0.01

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Textbook Question

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Textbook Question

Explain why the equation | x | = √x² has infinitely many solutions.

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Textbook Question

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Textbook Question

Solve each equation or inequality. |4x + 3| - 2 = -1

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Textbook Question

Solve each equation or inequality. |8 - 3x| - 3 = -2

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Textbook Question

Solve each equation or inequality. |6 - 2x | + 1 = 3

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Textbook Question

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Textbook Question

Solve each equation or inequality. | 4 - 4x | + 2 = 4

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Textbook Question

Solve each equation or inequality. | 3x + 1 | - 1 < 2

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Textbook Question

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Textbook Question

Solve each equation or inequality. | 5x + 2 | - 2 < 3

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Textbook Question

Solve each equation or inequality. | 5x + 1/2 | -2 < 5

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Textbook Question

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Textbook Question

Solve each equation or inequality. | 2x+ 1/3 | +1 < 4

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Textbook Question

Solve each equation or inequality. | 10 - 4x | + 1 ≥ 5

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Textbook Question

In Exercises 51–58, solve each compound inequality. 6 < x + 3 < 8

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Textbook Question

Solve each equation or inequality. | 12- 5x | + 3 ≥ 9

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Textbook Question

In Exercises 51–58, solve each compound inequality. - 3 ≤ x - 2 < 1

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Textbook Question

Solve each equation or inequality. | 3x- 7 | + 1 < -2

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Textbook Question

Solve each equation or inequality. |-5x + 7 | - 4 < -6

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Textbook Question

In Exercises 51–58, solve each compound inequality. - 11 < 2x - 1 ≤ - 5

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Textbook Question

Solve each equation or inequality. | 10- 4x | ≥ 4

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Textbook Question

Solve each equation or inequality. | 12- 9x | ≥ -12

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Textbook Question

Solve each equation or inequality. | 6- 3x | 4 < -11

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Textbook Question

In Exercises 51–58, solve each compound inequality. - 3 ≤ (2/3)x - 5 < - 1

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Textbook Question

Solve each equation or inequality. |18- 3x | 4 < -13

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Textbook Question

In Exercises 59–94, solve each absolute value inequality. |x| < 3

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Textbook Question

Solve each equation or inequality. | 8x + 5| = 0

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Textbook Question

Solve each equation or inequality. | 7 + 2x| = 0

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Textbook Question

Solve each equation or inequality. | 4.3x + 9.8| < 0

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Textbook Question

In Exercises 59–94, solve each absolute value inequality. |x - 1| ≤ 2

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Textbook Question

Solve each equation or inequality. | 1.5x - 14| < 0

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Textbook Question

In Exercises 59–94, solve each absolute value inequality. |x + 3| ≤ 4

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Textbook Question

In Exercises 59–94, solve each absolute value inequality. |2x - 6| < 8

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Textbook Question

In Exercises 59–94, solve each absolute value inequality. |3x + 5| < 17

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Textbook Question

In Exercises 59–94, solve each absolute value inequality. |2(x - 1) + 4| ≤ 8

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Textbook Question

Solve each equation or inequality. | 4x+ 3| > 0

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Textbook Question

In Exercises 59–94, solve each absolute value inequality. |3(x - 1)/4| < 6

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Textbook Question

Write each statement using an absolute value equation or inequality. . m is no more than 2 units from 7.

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Textbook Question

In Exercises 59–94, solve each absolute value inequality. |x| > 3

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Textbook Question

In Exercises 59–94, solve each absolute value inequality. |x - 1| ≥ 2

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Textbook Question

In Exercises 59–94, solve each absolute value inequality. |3x - 8| > 7

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Textbook Question

Write each statement using an absolute value equation or inequality. r is no less than 1 unit from 29.

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Textbook Question

Write each statement using an absolute value equation or inequality. q is no more than 8 units from 22.

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Textbook Question

In Exercises 59–94, solve each absolute value inequality. |(2x + 2)/4| ≥ 2

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Textbook Question

In Exercises 59–94, solve each absolute value inequality. |3 - (2/3)x| > 5

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Textbook Question

The temperatures on the surface of Mars in degrees Celsius approximately satisfy the inequality |C + 84 | ≤ 6. What range of temperatures corresponds to this inequality?

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Textbook Question

In Exercises 59–94, solve each absolute value inequality. 3|x - 1| + 2 ≥ 8

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Textbook Question

In Exercises 59–94, solve each absolute value inequality. 5|2x + 1| - 3 ≥ 9

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Textbook Question

In Exercises 59–94, solve each absolute value inequality. - 2|x - 4| ≥ - 4

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Textbook Question

In Exercises 59–94, solve each absolute value inequality. - 4|1 - x| < - 16

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Textbook Question

To see how to solve an equation that involves the absolute value of a quadratic polynomial, such as | x^2 - x | = 6, work Exercises 83–86 in order. For x^2 - x to have an absolute value equal to 6, what are the two possible values that x may assume? (Hint: One is positive and the other is negative.)

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Textbook Question

Solve each inequality. Give the solution set using interval notation. 11x≥2(x-4)

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Textbook Question

In Exercises 59–94, solve each absolute value inequality. 3 ≤ |2x - 1|

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Textbook Question

Solve each inequality. Give the solution set using interval notation. -5x - 4≥3(2x-5)

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Textbook Question

Solve each inequality. Give the solution set using interval notation. 7x-2(x-3) ≤5(2-x)

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Textbook Question

Use the method described in Exercises 83–86, if applicable, and properties of absolute value to solve each equation or inequality. (Hint: Exercises 99 and 100 can be solved by inspection.) | 3x^2 + x | = 14

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Textbook Question

Solve each inequality. Give the solution set using interval notation. 5 ≤ 2x -3 ≤ 7

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Textbook Question

In Exercises 59–94, solve each absolute value inequality. 5 > |4 - x|

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Textbook Question

Solve each inequality. Give the solution set using interval notation. -8 >3x-5>-12

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Textbook Question

In Exercises 59–94, solve each absolute value inequality. 1 < |2 - 3x|

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Textbook Question

In Exercises 59–94, solve each absolute value inequality. 12 < |- 2x + 6/7| + 3/7

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Textbook Question

In Exercises 59–94, solve each absolute value inequality. 4 + |3 - x/3| ≥ 9

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Textbook Question

In Exercises 95–102, use interval notation to represent all values of x satisfying the given conditions. y1 = x/2 + 3, y2 = x/3 + 5/2, and y1 ≤ y2

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Textbook Question

In Exercises 95–102, use interval notation to represent all values of x satisfying the given conditions. y1 = (2/3)(6x - 9) + 4, y2 = 5x + 1, and y1 > y2

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Textbook Question

In Exercises 95–102, use interval notation to represent all values of x satisfying the given conditions. y = 2x - 11 + 3(x + 2) and y is at most 0

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Textbook Question

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Textbook Question

In Exercises 95–102, use interval notation to represent all values of x satisfying the given conditions. y = |2x - 5| + 1 and y > 9

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Textbook Question

Solve and graph the solution set on a number line: 3|2x-1| ≥ 21

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Textbook Question

In Exercises 95–102, use interval notation to represent all values of x satisfying the given conditions. y = 8 - |5x + 3| and y is at least 6

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Textbook Question

In Exercises 103–104, use the graph of y = |4 - x| to solve each inequality.

|4 - x| ≥ 5

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Textbook Question

In Exercises 105–106, use the table to solve each inequality. - 3 < 2x - 5 ≤ 3

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Textbook Question

When 3 times a number is subtracted from 4, the absolute value of the difference is at least 5. Use interval notation to express the set of all numbers that satisfy this condition.

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Textbook Question

When 4 times a number is subtracted from 5, the absolute value of the difference is at most 13. Use interval notation to express the set of all numbers that satisfy this condition.

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Textbook Question

Solve and graph the solution set on a number line: (2x−3)/4 ≥ 3x/4 + 1/2

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Textbook Question

Solve each equation or inequality. |8-5x| ≥ 2

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Textbook Question

Solve each equation or inequality. |7x-3| > 4

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Textbook Question

Solve each equation or inequality. |7x+8| - 6 > -3

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Textbook Question

Solve each equation or inequality. |4x-12| ≥ -3

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Textbook Question

Write each statement using an absolute value equation or inequality. p is at least 3 units from 1.

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1. Equations & Inequalities

Linear Inequalities

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