Solving Inequalities and Compound Inequalities

Front

What is an inequality?

Back

An inequality is a mathematical statement that compares two expressions using symbols such as <, >, ≤, or ≥.

Front

What does it mean to solve an inequality?

Back

To solve an inequality means to find all values of the variable that make the inequality true.

Front

What is a compound inequality?

Back

A compound inequality combines two or more inequalities using '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 graph an inequality on a number line?

Back

To graph an inequality, use an open circle for < or > and a closed circle for ≤ or ≥, then shade the appropriate region.

Front

What is the solution to the inequality x + 2 < -4?

Back

x < -6.

Front

What is the solution to the inequality -5x < -15?

Back

x > 3.

Front

What is the solution to the compound inequality 2x - 8 ≤ 4 and x + 5 ≥ 7?

Back

2 ≤ x ≤ 6.

Front

What is the solution to the compound inequality -2 < 3x - 5 ≤ 4?

Back

1 < x ≤ 3.