Solving Compound Inequalities

Front

What is a compound inequality?

Back

A compound inequality is an inequality that combines two or more simple inequalities using the words 'and' or 'or'.

Front

How do you solve a compound inequality with 'or'?

Back

To solve a compound inequality with 'or', solve each inequality separately and combine the solutions.

Front

How do you solve a compound inequality with 'and'?

Back

To solve a compound inequality with 'and', find the intersection of the solution sets of the individual inequalities.

Front

What does the symbol '≤' mean?

Back

The symbol '≤' means 'less than or equal to'.

Front

What does the symbol '≥' mean?

Back

The symbol '≥' means 'greater than or equal to'.

Front

Solve the compound inequality: x + 8 < 3 or -8x < -40.

Back

x < -5 or x > 5.

Front

Solve the compound inequality: -3 ≤ 2x - 1 ≤ 5.

Back

-1 ≤ x ≤ 3.

Front

Solve the compound inequality: -4x + 1 ≤ 21 and 5x + 2 < 22.

Back

x ≥ -5 and x < 4.

Front

What is the solution set for the inequality: -13 < 2x + 5 < 15?

Back

-9 < x < 5.

Front

What is the first step in solving a compound inequality?

Back

Identify whether the compound inequality uses 'and' or 'or' and separate the inequalities.