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More Lessons for Basic Algebra

Math Worksheets

A series of free Basic Algebra Lessons.

**How to Solve and Graph Compound Inequalities**

In mathematics, it can be useful limit the solution or even have multiple solutions for an inequality. For this we use compound inequalities, inequalities with multiple inequality signs. When solving compound inequalities, we use some of the same methods used in solving multi-step inequalities. However, when we multiply or divide by a negative, we must reverse the inequality symbol. The solutions to compound inequalities can be graphed on a number line, and can be expressed as intervals.

**Solve a Compound Inequality Involving AND (Intersection)**

This video provides an example of how to solve a compound inequality involving AND or the intersection of two inequalities. The solution is also written using interval notation.

Example:

Solve the compound inequality and express using interval notation.

-1 < 2x - 5 ≤ 3

**Solve a Compound Inequality Involving AND (Intersection)**

This video provides an example of how to solve a compound inequality involving AND or the intersection of two inequalities. The solution is also written using interval notation.

Example:

Solve the compound inequality and express using interval notation.

-13 < 3 - 4x ≤ 1

**Solve a Compound Inequality Involving AND (Intersection)**

This video provides an example of how to solve a compound inequality involving AND or the intersection of two inequalities. The solution is also written using interval notation.

Example:

Solve the compound inequality and express using interval notation.

2x + 10 < x + 9 ≤ 3x + 15

**Solve a Compound Inequality (No Solution)**

This video provides an example a compound inequality involving AND or Intersection with no solution.

Example:

Solve the compound inequality and express using interval notation.

2x - 3 < -3 AND -4x - 2 < -14

**Solve a Multiple Step Compound Inequality (OR / Union)**

This video provides an example of how to solve a multiple step compound inequality involving OR or the Union of two inequalities. The solution is also written using interval notation.

Example:

Solve the compound inequality and express using interval notation.

15x - 3 > 9x + 15 OR -23 + 4x ≥ 12x + 1

**Solve a Compound Inequality Involving OR (Union)**

This video provides an example of how to solve a compound inequality involving OR or the union of two inequalities. The solution is also written using interval notation.

Example:

Solve the compound inequality and express using interval notation.

2x - 10 < -14 OR -3x + 2 < -10

**Solve a Multiple Step Compound Inequality (OR / Union)**

This video provides an example of how to solve a multiple step compound inequality involving OR or the Union of two inequalities. The solution is also written using interval notation.

Example:

Solve the compound inequality and express using interval notation.

15x - 3 > 9x + 15 )R -23 + 4x ≥ 12x + 1

**Solve a Compound Inequality (All Real Numbers Solution)**

This video provides an example of how to solve a compound inequality involving OR or the Union of two inequalities with a solution of all real numbers. The solution is also written using interval notation.

Example:

Solve the compound inequality and express using interval notation.

5x - 12 < 8 OR -2x + 1 ≤ -5

You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

More Lessons for Basic Algebra

Math Worksheets

A series of free Basic Algebra Lessons.

In this lesson, we will learn

- how to solve compound inequalities involving AND or Intersection
- how to solve compound inequalities involving OR or Union

In mathematics, it can be useful limit the solution or even have multiple solutions for an inequality. For this we use compound inequalities, inequalities with multiple inequality signs. When solving compound inequalities, we use some of the same methods used in solving multi-step inequalities. However, when we multiply or divide by a negative, we must reverse the inequality symbol. The solutions to compound inequalities can be graphed on a number line, and can be expressed as intervals.

This video provides an example of how to solve a compound inequality involving AND or the intersection of two inequalities. The solution is also written using interval notation.

Example:

Solve the compound inequality and express using interval notation.

-1 < 2x - 5 ≤ 3

This video provides an example of how to solve a compound inequality involving AND or the intersection of two inequalities. The solution is also written using interval notation.

Example:

Solve the compound inequality and express using interval notation.

-13 < 3 - 4x ≤ 1

This video provides an example of how to solve a compound inequality involving AND or the intersection of two inequalities. The solution is also written using interval notation.

Example:

Solve the compound inequality and express using interval notation.

2x + 10 < x + 9 ≤ 3x + 15

This video provides an example a compound inequality involving AND or Intersection with no solution.

Example:

Solve the compound inequality and express using interval notation.

2x - 3 < -3 AND -4x - 2 < -14

This video provides an example of how to solve a multiple step compound inequality involving OR or the Union of two inequalities. The solution is also written using interval notation.

Example:

Solve the compound inequality and express using interval notation.

15x - 3 > 9x + 15 OR -23 + 4x ≥ 12x + 1

This video provides an example of how to solve a compound inequality involving OR or the union of two inequalities. The solution is also written using interval notation.

Example:

Solve the compound inequality and express using interval notation.

2x - 10 < -14 OR -3x + 2 < -10

This video provides an example of how to solve a multiple step compound inequality involving OR or the Union of two inequalities. The solution is also written using interval notation.

Example:

Solve the compound inequality and express using interval notation.

15x - 3 > 9x + 15 )R -23 + 4x ≥ 12x + 1

This video provides an example of how to solve a compound inequality involving OR or the Union of two inequalities with a solution of all real numbers. The solution is also written using interval notation.

Example:

Solve the compound inequality and express using interval notation.

5x - 12 < 8 OR -2x + 1 ≤ -5

Rotate to landscape screen format on a mobile phone or small tablet to use the **Mathway** widget, a free math problem solver that **answers your questions with step-by-step explanations**.

You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

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