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 'and' mean in a compound inequality?

Back

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

Front

What does 'or' mean in a compound inequality?

Back

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

Front

How do you solve the compound inequality 0 < x + 7 < 9?

Back

Subtract 7 from all parts: -7 < x < 2.

Front

What is the solution set for the inequality -7 < x < 2?

Back

The solution set is all real numbers between -7 and 2, not including -7 and 2.

Front

How do you graph the solution of a compound inequality?

Back

Use open circles for non-inclusive endpoints and shade the region between or outside the circles depending on 'and' or 'or'.

Front

What is the difference between 'x > 5' and 'x ≥ 5'?

Back

'x > 5' means x is greater than 5, while 'x ≥ 5' means x is greater than or equal to 5.

Front

Solve the inequality -2(x + 2) < 14.

Back

Distribute: -2x - 4 < 14; then add 4: -2x < 18; divide by -2: x > -9.

Front

What does the graph of 'x ≤ -2 OR x > 5' look like?

Back

It has a closed circle at -2 and an open circle at 5, with shading to the left of -2 and to the right of 5.

Front

What is the solution to the compound inequality x > 5 OR x < -2?

Back

The solution includes all numbers greater than 5 and all numbers less than -2.