Compound Inequalities

Front

What is a compound inequality?

Back

A compound inequality combines two or more inequalities using 'and' or 'or'.

Front

What does the symbol '≤' mean?

Back

It means 'less than or equal to'.

Front

What does the symbol '≥' mean?

Back

It means 'greater than or equal to'.

Front

When do you use a closed dot on a graph?

Back

You use a closed dot when the inequality includes '≤' or '≥'.

Front

When do you use an open dot on a graph?

Back

You use an open dot when the inequality includes '<' or '>'.

Front

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

Back

The solution set is 1 < x < 3.

Front

What is the solution set for the inequality x ≤ -2 or x > 5?

Back

The solution set includes all numbers less than or equal to -2 and all numbers greater than 5.

Front

How do you solve the compound inequality -4x + 1 ≤ 21 and 5x + 2 < 22?

Back

First, solve each inequality separately: -4x ≤ 20 gives x ≥ -5; 5x < 20 gives x < 4. The final solution is x ≥ -5 and x < 4.

Front

How do you solve the compound inequality 3x + 2 < -7 or -4x + 5 < 1?

Back

First, solve each inequality separately: 3x < -9 gives x < -3; -4x < -4 gives x > 1. The final solution is x < -3 or x > 1.

Front

What is the graph of the inequality -2 ≤ x ≤ 5?

Back

The graph includes a closed dot at -2 and a closed dot at 5, with a line connecting them.