# Linear Inequalities - Video Tutorials & Practice Problems

## Interval Notation

Express the given set in interval notation and graph.

{$x$ | 14 ≤ $x$ < 26}

(14,26)

[14,26]

[14, 26)

(14,26]

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

{$x\left|x\right.$ ≤ 0}

{$x\mid x$ < 0}

{$x\mid x$ > 0}

$\left\lbrace x|x\ge0\right\rbrace$

Express the given set in interval notation and graph.

$\{$$x$ $\mid $$x\le 7$$\}$

(−∞,7]

[−∞,7]

(−∞,7)

[7, ∞)

## Linear Inequalities

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

$\left(-\infty,\frac72\right)$

$\left(-\infty,\frac72\right]$

$\left[\frac72,\infty\right)$

$\left(\frac72,\infty\right)$

## Linear Inequalities with Fractions & Variables on Both Sides

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

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

$\left(-4,\infty\right)$

$\left[4,\infty\right)$

$\left[-4,\infty\right)$

$\left(-\infty,-4]\right.$

## Do you want more practice?

- Match each equation or inequality in Column I with the graph of its solution set in Column II. | x | = 7
- Match the inequality in each exercise in Column I with its equiva-lent interval notation in Column II. x<-6
- In Exercises 1–14, express each interval in set-builder notation and graph the interval on a number line. (1,...
- Match each equation or inequality in Column I with the graph of its solution set in Column II. | x | = -7
- Match the inequality in each exercise in Column I with its equiva-lent interval notation in Column II. x≤6
- Match the inequality in each exercise in Column I with its equiva-lent interval notation in Column II. -2
- In Exercises 1–14, express each interval in set-builder notation and graph the interval on a number line. [- ...
- Match each equation or inequality in Column I with the graph of its solution set in Column II. | x | > -7
- Match the inequality in each exercise in Column I with its equiva-lent interval notation in Column II. x^2≥0
- Match each equation or inequality in Column I with the graph of its solution set in Column II. | x | > 7
- Match the inequality in each exercise in Column I with its equiva-lent interval notation in Column II . x≥-6
- Match each equation or inequality in Column I with the graph of its solution set in Column II. | x | < 7
- In Exercises 1–14, express each interval in set-builder notation and graph the interval on a number line. [- ...
- Match the inequality in each exercise in Column I with its equiva-lent interval notation in Column II. 6≤x
- Match each equation or inequality in Column I with the graph of its solution set in Column II. | x | ≥ 7
- Match each equation or inequality in Column I with the graph of its solution set in Column II. | x | ≤ 7
- In Exercises 1–14, express each interval in set-builder notation and graph the interval on a number line. (2,...
- Match each equation or inequality in Column I with the graph of its solution set in Column II. | x | ≠ 7
- In Exercises 1–14, express each interval in set-builder notation and graph the interval on a number line. [- ...
- In Exercises 1–14, express each interval in set-builder notation and graph the interval on a number line. (- ...
- In Exercises 1–14, express each interval in set-builder notation and graph the interval on a number line. (- ...
- In Exercises 15–26, use graphs to find each set. (- 3, 0) ∩ [- 1, 2]
- In Exercises 15–26, use graphs to find each set. (- 3, 0) ⋃ [- 1, 2]
- Solve each inequality. Give the solution set in interval notation. See Examples 1 and 2. 3(x+5)+1≥5+3x
- In Exercises 15–26, use graphs to find each set. (- ∞, 5) ∩ [1, 8)
- Solve each inequality. Give the solution set in interval notation. See Examples 1 and 2. 8x-3x+2<2(x+7)
- Solve each inequality. Give the solution set in interval notation. See Examples 1 and 2. 2-4x+5(x-1)<-6(x-2...
- Solve each inequality. Give the solution set in interval notation. See Examples 1 and 2. (4x+7)/-3≤2x+5
- In Exercises 15–26, use graphs to find each set. (- ∞, 5) ⋃ [1, 8)
- Solve each inequality. Give the solution set in interval notation. See Examples 1 and 2. (2x-5)/-8≤1-x
- Solve each inequality. Give the solution set in interval notation. See Examples 1 and 2. (1/3)x+(2/5)x-(1/2)(x...
- In Exercises 15–26, use graphs to find each set. [3, ∞) ∩ (6, ∞)
- Solve each inequality. Give the solution set in interval notation. See Examples 1 and 2. -(2/3)x-(1/6)x+(2/3)(...
- In Exercises 15–26, use graphs to find each set. [3, ∞) ⋃ (6, ∞)
- In all exercises, other than exercises with no solution, use interval notation to express solution sets and gr...
- Solve each inequality. Give the solution set in interval notation. | 3x - 4 | < 2
- Solve each inequality. Give the solution set in interval notation. See Example 4. -5<5+2x<11
- In all exercises, other than exercises with no solution, use interval notation to express solution sets and gr...
- Solve each inequality. Give the solution set in interval notation. . | 3x - 4 | ≥ 2
- Solve each inequality. Give the solution set in interval notation. | 1/2 - x | ≤ 2
- In all exercises, other than exercises with no solution, use interval notation to express solution sets and gr...
- Solve each inequality. Give the solution set in interval notation. See Example 4. 10≤2x+4≤16
- Solve each inequality. Give the solution set in interval notation. | 3/5 + x | < 1
- Solve each inequality. Give the solution set in interval notation. See Example 4. 2>-6x+3>-3
- Solve each inequality. Give the solution set in interval notation. 5| x + 1 | > 10
- Solve each inequality. Give the solution set in interval notation. See Example 4. -4≤(x+1)/2≤5
- Solve each inequality. Give the solution set in interval notation. | 5 - 3x | > 7
- Solve each inequality. Give the solution set in interval notation. | 7 - 3x | > 4
- Solve each inequality. Give the solution set in interval notation. | 5 - 3x | ≤ 7
- Solve each inequality. Give the solution set in interval notation. See Example 4. 1≤(4x-5)/2<9
- Solve each inequality. Give the solution set in interval notation. | 7 - 3x | ≤ 4
- Solve each inequality. Give the solution set in interval notation. | (2/3)x + 1/2 | ≤ 1/6
- Solve each inequality. Give the solution set in interval notation. | 5/3 - (1/2) x | > 2/9
- Solve each inequality. Give the solution set in interval notation. | 0.01x + 1 | < 0.01
- Explain why the equation | x | = √x² has infinitely many solutions.
- Solve each equation or inequality. |4x + 3| - 2 = -1
- Solve each equation or inequality. |8 - 3x| - 3 = -2
- Solve each equation or inequality. |6 - 2x | + 1 = 3
- Solve each equation or inequality. | 4 - 4x | + 2 = 4
- Solve each equation or inequality. | 3x + 1 | - 1 < 2
- Solve each equation or inequality. | 5x + 2 | - 2 < 3
- Solve each equation or inequality. | 5x + 1/2 | -2 < 5
- Solve each equation or inequality. | 2x+ 1/3 | +1 < 4
- Solve each equation or inequality. | 10 - 4x | + 1 ≥ 5
- In Exercises 51–58, solve each compound inequality. 6 < x + 3 < 8
- Solve each equation or inequality. | 12- 5x | + 3 ≥ 9
- In Exercises 51–58, solve each compound inequality. - 3 ≤ x - 2 < 1
- Solve each equation or inequality. | 3x- 7 | + 1 < -2
- Solve each equation or inequality. |-5x + 7 | - 4 < -6
- In Exercises 51–58, solve each compound inequality. - 11 < 2x - 1 ≤ - 5
- Solve each equation or inequality. | 10- 4x | ≥ 4
- Solve each equation or inequality. | 12- 9x | ≥ -12
- Solve each equation or inequality. | 6- 3x | 4 < -11
- In Exercises 51–58, solve each compound inequality. - 3 ≤ (2/3)x - 5 < - 1
- Solve each equation or inequality. |18- 3x | 4 < -13
- In Exercises 59–94, solve each absolute value inequality. |x| < 3
- Solve each equation or inequality. | 8x + 5| = 0
- Solve each equation or inequality. | 7 + 2x| = 0
- Solve each equation or inequality. | 4.3x + 9.8| < 0
- In Exercises 59–94, solve each absolute value inequality. |x - 1| ≤ 2
- Solve each equation or inequality. | 1.5x - 14| < 0
- In Exercises 59–94, solve each absolute value inequality. |x + 3| ≤ 4
- In Exercises 59–94, solve each absolute value inequality. |2x - 6| < 8
- In Exercises 59–94, solve each absolute value inequality. |3x + 5| < 17
- In Exercises 59–94, solve each absolute value inequality. |2(x - 1) + 4| ≤ 8
- Solve each equation or inequality. | 4x+ 3| > 0
- In Exercises 59–94, solve each absolute value inequality. |3(x - 1)/4| < 6
- Write each statement using an absolute value equation or inequality. . m is no more than 2 units from 7.
- In Exercises 59–94, solve each absolute value inequality. |x| > 3
- In Exercises 59–94, solve each absolute value inequality. |x - 1| ≥ 2
- In Exercises 59–94, solve each absolute value inequality. |3x - 8| > 7
- Write each statement using an absolute value equation or inequality. r is no less than 1 unit from 29.
- Write each statement using an absolute value equation or inequality. q is no more than 8 units from 22.
- In Exercises 59–94, solve each absolute value inequality. |(2x + 2)/4| ≥ 2
- In Exercises 59–94, solve each absolute value inequality. |3 - (2/3)x| > 5
- The temperatures on the surface of Mars in degrees Celsius approximately satisfy the inequality |C + 84 | ≤ 6....
- In Exercises 59–94, solve each absolute value inequality. 3|x - 1| + 2 ≥ 8
- In Exercises 59–94, solve each absolute value inequality. 5|2x + 1| - 3 ≥ 9
- In Exercises 59–94, solve each absolute value inequality. - 2|x - 4| ≥ - 4
- In Exercises 59–94, solve each absolute value inequality. - 4|1 - x| < - 16
- To see how to solve an equation that involves the absolute value of a quadratic polynomial, such as | x^2 - x ...
- Solve each inequality. Give the solution set using interval notation. 11x≥2(x-4)
- In Exercises 59–94, solve each absolute value inequality. 3 ≤ |2x - 1|
- Solve each inequality. Give the solution set using interval notation. -5x - 4≥3(2x-5)
- Solve each inequality. Give the solution set using interval notation. 7x-2(x-3) ≤5(2-x)
- Use the method described in Exercises 83–86, if applicable, and properties of absolute value to solve each equ...
- Solve each inequality. Give the solution set using interval notation. 5 ≤ 2x -3 ≤ 7
- In Exercises 59–94, solve each absolute value inequality. 5 > |4 - x|
- Solve each inequality. Give the solution set using interval notation. -8 >3x-5>-12
- In Exercises 59–94, solve each absolute value inequality. 1 < |2 - 3x|
- In Exercises 59–94, solve each absolute value inequality. 12 < |- 2x + 6/7| + 3/7
- In Exercises 59–94, solve each absolute value inequality. 4 + |3 - x/3| ≥ 9
- In Exercises 95–102, use interval notation to represent all values of x satisfying the given conditions. y1 =...
- In Exercises 95–102, use interval notation to represent all values of x satisfying the given conditions. y1 =...
- In Exercises 95–102, use interval notation to represent all values of x satisfying the given conditions. y = ...
- Use the method described in Exercises 83–86, if applicable, and properties of absolute value to solve each equ...
- In Exercises 95–102, use interval notation to represent all values of x satisfying the given conditions. y = ...
- Solve and graph the solution set on a number line: 3|2x-1| ≥ 21
- In Exercises 95–102, use interval notation to represent all values of x satisfying the given conditions. y = ...
- In Exercises 103–104, use the graph of y = |4 - x| to solve each inequality. |4 - x| ≥ 5
- In Exercises 105–106, use the table to solve each inequality. - 3 < 2x - 5 ≤ 3
- When 3 times a number is subtracted from 4, the absolute value of the difference is at least 5. Use interval n...
- When 4 times a number is subtracted from 5, the absolute value of the difference is at most 13. Use interval n...
- Solve and graph the solution set on a number line: (2x−3)/4 ≥ 3x/4 + 1/2
- Solve each equation or inequality. |8-5x| ≥ 2
- Solve each equation or inequality. |7x-3| > 4
- Solve each equation or inequality. |7x+8| - 6 > -3
- Solve each equation or inequality. |4x-12| ≥ -3
- Write each statement using an absolute value equation or inequality. p is at least 3 units from 1.