2.5 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

What does 'or' mean in a compound inequality?

Back

In a compound inequality, 'or' indicates that at least one of the inequalities must be true.

Front

What does 'and' mean in a compound inequality?

Back

In a compound inequality, 'and' indicates that both inequalities must be true at the same time.

Front

Solve the compound inequality: 3x − 4 < −13 or 7x + 1 > 22.

Back

x < −3 or x > 3.

Front

What is the solution to the inequality -4x + 14 ≤ 54?

Back

x ≥ -10.

Front

What inequality is represented by the graph showing x ≥ -5?

Back

x ≥ -5.

Front

How do you solve the inequality 2x + 3 > 7?

Back

Subtract 3 from both sides: 2x > 4, then divide by 2: x > 2.

Front

What is the solution to the compound inequality: x > 2 or x ≤ −3?

Back

The solution includes all values greater than 2 and all values less than or equal to -3.

Front

What does the solution x < -3 or x > 3 represent on a number line?

Back

It represents two separate regions: all numbers less than -3 and all numbers greater than 3.

Front

If x + 5 < 10, what is the solution?

Back

x < 5.