Compound Inequalities

Front

Define compound inequality.

Back

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

Front

What does the symbol '≤' represent in inequalities?

Back

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

Front

What does the symbol '≥' represent in inequalities?

Back

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

Front

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

Back

-1 ≤ x ≤ 3.

Front

Solve the compound inequality: -13 < 2x + 5 < 15.

Back

-9 < x < 5.

Front

When graphing an inequality, what does a closed dot indicate?

Back

A closed dot indicates that the endpoint is included in the solution (used with ≤ or ≥).

Front

When graphing an inequality, what does an open dot indicate?

Back

An open dot indicates that the endpoint is not included in the solution (used with < or >).

Front

Solve the inequality: 3x + 2 < -7 or -4x + 5 < 1.

Back

x < -3 or x > 1.

Front

What is the solution set for the inequality x < -3 or x > 1?

Back

The solution set includes all numbers less than -3 and all numbers greater than 1.

Front

How do you solve a compound inequality?

Back

To solve a compound inequality, isolate the variable in the middle and solve each part of the inequality.