2. Equations and Inequalities

Find Intersections and Unions of Intervals

Linear Inequalities and Absolute Value Inequalities

Union and intersection of intervals

Finding the union and intersections of intervals examples

In Exercises 59–94, solve each absolute value inequality.

- 2|x - 4| ≥ - 4

Solve inequalities with negative coefficients: dividing by negatives

In Exercises 59–94, solve each absolute value inequality.

|3x - 8| > 7

Solving inequalities with no solution or all real numbers as solutions

In Exercises 95–102, use interval notation to represent all values of x satisfying the given conditions.

y = |2x - 5| + 1 and y > 9

In Exercises 59–94, solve each absolute value inequality.

5 > |4 - x|

❖ Solving Linear Inequalities Made Easy ❖

In Exercises 59–94, solve each absolute value inequality.

|3 - (2/3)x| > 5

In Exercises 59–94, solve each absolute value inequality.

12 < |- 2x + 6/7| + 3/7

In Exercises 59–94, solve each absolute value inequality.

|(2x + 2)/4| ≥ 2

Using Interval Notation to Express Inequalities - Example 1

Interval Notation - A basic question!

In Exercises 59–94, solve each absolute value inequality.

|2(x - 1) + 4| ≤ 8

In Exercises 59–94, solve each absolute value inequality.

- 4|1 - x| < - 16

In Exercises 15–26, use graphs to find each set.

(- ∞, 5) ⋃ [1, 8)

An Introduction To Solving Linear Inequalities - Example 1

Solving Word Problems Involving Inequalities - Example 3

Solving Absolute Value Inequalities - Example 1

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

Solve compound conjunction inequalities with 1 variable

In Exercises 15–26, use graphs to find each set.

(- 3, 0) ∩ [- 1, 2]

In Exercises 59–94, solve each absolute value inequality.

|2x - 6| < 8

An Introduction To Solving Linear Inequalities - Example 2

Using Interval Notation to Express Inequalities - Example 2

Writing Compound Inequalities Using Interval Notation - Example 2

Definition and Technique For Solving Linear Inequalities

Solve No Solution and All Real Number Inequalities

Drawing a Number Line to Match an Inequality

Solving Inequalities with No Solution or Infinite Solutions

Interval Notation

Inequalities with No Solution or All Real Numbers

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.

Solving Absolute Value Inequalities, MORE Examples - Example 2

Solving A Compound Linear Inequality

In Exercises 59–94, solve each absolute value inequality.

|x| > 3

In Exercises 59–94, solve each absolute value inequality.

|3x + 5| < 17

In Exercises 15–26, use graphs to find each set.

[3, ∞) ⋃ (6, ∞)

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.

Solve inequalities with 1 variable: graphing on a number line

In Exercises 59–94, solve each absolute value inequality.

|x| < 3

In Exercises 59–94, solve each absolute value inequality.

4 + |3 - x/3| ≥ 9

In Exercises 59–94, solve each absolute value inequality.

|x + 3| ≤ 4

In Exercises 15–26, use graphs to find each set.

(- 3, 0) ⋃ [- 1, 2]

In Exercises 51–58, solve each compound inequality.

6 < x + 3 < 8

In Exercises 15–26, use graphs to find each set.

[3, ∞) ∩ (6, ∞)

Intersections & Unions of Intervals

Absolute Value Inequalities - How to Solve

In Exercises 59–94, solve each absolute value inequality.

|3(x - 1)/4| < 6

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

Solve absolute value disjunction inequalities

Linear Inequalities

Solving Two - Step Linear Inequalities

Solving Word Problems Involving Inequalities - Example 2

Solve absolute value conjunction inequalities

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

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

In Exercises 51–58, solve each compound inequality.

- 3 ≤ x - 2 < 1

Solving 3 Basic Linear Inequalities

Solve compound disjunction inequalities with 1 variable

In Exercises 59–94, solve each absolute value inequality.

|x - 1| ≤ 2

Solving Algebraic Inequalities

An Introduction To Solving Linear Inequalities - Example 3

In Exercises 51–58, solve each compound inequality.

- 3 ≤ (2/3)x - 5 < - 1

Solving Basic Linear Inequalities Involving Multiplication or Division

In Exercises 15–26, use graphs to find each set.

(- ∞, 5) ∩ [1, 8)

In Exercises 51–58, solve each compound inequality.

- 11 < 2x - 1 ≤ - 5

In Exercises 59–94, solve each absolute value inequality.

1 < |2 - 3x|

Solving Linear Absolute Value Equations and Inequalities

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College Algebra

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