Multi-step Inequalities

Front

What is a multi-step inequality?

Back

A multi-step inequality is an inequality that requires more than one step to solve, often involving combining like terms, distributing, and isolating the variable.

Front

How do you solve the inequality 7(x + 3) < 5x + 13?

Back

First, distribute: 7x + 21 < 5x + 13. Then, subtract 5x from both sides: 2x + 21 < 13. Next, subtract 21: 2x < -8. Finally, divide by 2: x < -4.

Front

What does the solution x < -4 represent?

Back

It means that any value of x that is less than -4 will satisfy the inequality.

Front

How do you solve the inequality 28 - k ≥ 7(k - 4)?

Back

First, distribute: 28 - k ≥ 7k - 28. Then, add k to both sides: 28 ≥ 8k - 28. Next, add 28: 56 ≥ 8k. Finally, divide by 8: 7 ≥ k or k ≤ 7.

Front

What does the solution k ≤ 7 indicate?

Back

It indicates that k can be any value less than or equal to 7.

Front

Write an inequality for Sue's lunch account compared to Troy's lunch account.

Back

25 - 2.5d > 50 - 3.25d.

Front

What does the inequality 25 - 2.5d > 50 - 3.25d represent?

Back

It shows the number of days (d) after which Sue's lunch account will have more money than Troy's.

Front

How do you set up the inequality for spending on a laptop?

Back

12x + 400 < 1200.

Front

What does the inequality 12x + 400 < 1200 mean?

Back

It means that after making a $400 down payment, the total monthly payments (12x) must be less than $800.

Front

Solve the inequality 9 + 4x > 21.

Back

Subtract 9 from both sides: 4x > 12. Then divide by 4: x > 3.