Solving Inequalities Review

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 3(d + 2) < -15?

Back

First, distribute: 3d + 6 < -15. Then, subtract 6: 3d < -21. Finally, divide by 3: d < -7.

Front

What does the solution d < -7 represent?

Back

It means that d can take any value less than -7.

Front

Solve the inequality -4(-7 - 5x) > 188.

Back

Distribute: 28 + 20x > 188. Subtract 28: 20x > 160. Divide by 20: x > 8.

Front

What does the solution x > 8 indicate?

Back

It means that x can take any value greater than 8.

Front

How do you solve the inequality 4 - 7y ≤ 18?

Back

Subtract 4: -7y ≤ 14. Divide by -7 (remember to flip the inequality): y ≥ -2.

Front

What does the solution y ≥ -2 mean?

Back

It means that y can take any value greater than or equal to -2.

Front

Solve the inequality -8x < 48.

Back

Divide by -8 (flip the inequality): x > -6.

Front

What does x > -6 signify?

Back

It means that x can take any value greater than -6.

Front

Write an inequality for spending time on homework problems if you have 30 minutes for 12 problems.

Back

12x ≤ 30, where x is the time spent per problem.