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 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 numbers greater than -22, extending to the right on the number line.

Front

What is the first step to solve -4x + 14 ≤ 54?

Back

Subtract 14 from both sides: -4x ≤ 40.

Front

How do you isolate x in the inequality -4x ≤ 40?

Back

Divide both sides by -4, remembering to flip the inequality sign: x ≥ -10.

Front

What does the solution x ≥ -10 indicate?

Back

It indicates that x can be any number greater than or equal to -10.

Front

Solve the inequality 4(2a + 3) < 3(a - 1).

Back

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

Front

What is the solution to the inequality 3(y + 1) ≥ -6?

Back

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

Front

What does the solution y ≥ -3 mean in context?

Back

It means y can be any number greater than or equal to -3.

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.