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 operations such as addition, subtraction, multiplication, or division.

Front

How do you solve the inequality 4(2a + 3) < 3(a - 1)?

Back

First, distribute: 8a + 12 < 3a - 3. Then, subtract 3a from both sides: 5a + 12 < -3. Next, subtract 12: 5a < -15. Finally, divide by 5: a < -3.

Front

What does the solution a < -3 represent on a number line?

Back

It represents all numbers to the left of -3, not including -3 itself.

Front

How do you solve the inequality 14 < -2a + 6 - 2a?

Back

Combine like terms: 14 < -4a + 6. Subtract 6 from both sides: 8 < -4a. Divide by -4 (remember to flip the inequality): a < -2.

Front

What does the solution a < -2 indicate about the values of a?

Back

It indicates that a can be any number less than -2.

Front

How do you solve the inequality 3(x + 2) + 13 > 55?

Back

Distribute: 3x + 6 + 13 > 55. Combine like terms: 3x + 19 > 55. Subtract 19: 3x > 36. Divide by 3: x > 12.

Front

What does the solution x > 12 mean in terms of possible values for x?

Back

It means x can be any number greater than 12.

Front

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

Back

Distribute: 28 - k ≥ 7k - 28. Add k to both sides: 28 ≥ 8k - 28. Add 28: 56 ≥ 8k. Divide by 8: 7 ≥ k or k ≤ 7.

Front

What does the solution k ≤ 7 signify?

Back

It signifies that k can be any number less than or equal to 7.

Front

How do you solve the inequality 3(y + 1) ≥ -6?

Back

Distribute: 3y + 3 ≥ -6. Subtract 3: 3y ≥ -9. Divide by 3: y ≥ -3.