Solving Inequalities

Front

What does the inequality x ≥ -5 mean?

Back

The value of x is greater than or equal to -5.

Front

How do you solve the inequality -4x + 14 ≤ 54?

Back

Subtract 14 from both sides: -4x ≤ 40. Then divide by -4 (remember to flip the inequality): x ≥ -10.

Front

What is the solution to the inequality 5z - 2 - 2z < 13?

Back

Combine like terms: 3z - 2 < 13. Add 2 to both sides: 3z < 15. Divide by 3: z < 5.

Front

When do you flip the inequality symbol?

Back

You flip the inequality symbol when you multiply or divide both sides by a negative number.

Front

What does the number line graph for x > 5 look like?

Back

An open circle at 5 and a line extending to the right.

Front

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

Back

x ≥ 5 includes 5, while x > 5 does not include 5.

Front

How do you graph the inequality x < 3?

Back

Draw an open circle at 3 and shade to the left.

Front

What is the solution set for the inequality 2x + 3 > 7?

Back

Subtract 3 from both sides: 2x > 4. Divide by 2: x > 2.

Front

What does the inequality x ≤ 4 represent on a number line?

Back

A closed circle at 4 and a line extending to the left.

Front

How do you solve the inequality 3x - 5 < 10?

Back

Add 5 to both sides: 3x < 15. Divide by 3: x < 5.