 # Compound Inequalities

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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

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

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