Practice Problems Lesson 1 to 3

Front

What is an inequality?

Back

An inequality is a mathematical statement that compares two expressions and shows that one is greater than, less than, or not equal to the other. Examples include <, >, ≤, and ≥.

Front

How do you solve the inequality 5z - 2 - 2z < 13?

Back

Combine like terms: 3z - 2 < 13. Then add 2 to both sides: 3z < 15. Finally, divide by 3: z < 5.

Front

What does the solution z < 5 represent on a number line?

Back

It represents all values to the left of 5, not including 5 itself.

Front

What is the solution to 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 represent on a number line?

Back

It represents all values to the right of -2, not including -2 itself.

Front

How do you solve the inequality 6x + 10 > 5x - 12?

Back

Subtract 5x from both sides: x + 10 > -12. Then subtract 10: x > -22.

Front

What does the solution x > -22 represent on a number line?

Back

It represents all values to the right of -22, not including -22 itself.

Front

What inequality does the number line graph x < -4 represent?

Back

It indicates that the values of x are less than -4.

Front

How do you solve the inequality -24 + k ≤ 10?

Back

Add 24 to both sides: k ≤ 34.

Front

What does the solution k ≤ 34 represent on a number line?

Back

It represents all values to the left of 34, including 34 itself.