Solving and Graphing Inequalities

Front

What is an inequality?

Back

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

Front

How do you solve the inequality x + 5 ≤ 13?

Back

Subtract 5 from both sides: x ≤ 8.

Front

What does the solution x ≤ 8 represent on a number line?

Back

It represents all numbers to the left of 8, including 8 itself.

Front

How do you solve the inequality -7 + 10z > -27?

Back

Add 7 to both sides: 10z > -20; then divide by 10: z > -2.

Front

What does the solution z > -2 mean?

Back

It means z can be any number greater than -2.

Front

How do you solve the inequality 10 < 3x + 19?

Back

Subtract 19 from both sides: -9 < 3x; then divide by 3: x > -3.

Front

What does the solution x > -3 indicate?

Back

It indicates that x can be any number greater than -3.

Front

How do you solve the inequality 30 + x ≥ 50?

Back

Subtract 30 from both sides: x ≥ 20.

Front

What does the solution x ≥ 20 signify?

Back

It signifies that x can be 20 or any number greater than 20.

Front

How do you solve the inequality 10 ≥ x - 3?

Back

Add 3 to both sides: 13 ≥ x; or x ≤ 13.