P4: 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 from both sides: 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

How do you solve the inequality -3(9 + x) ≥ -21?

Back

Distribute: -27 - 3x ≥ -21. Add 27 to both sides: -3x ≥ 6. Divide by -3 (remember to flip the inequality): x ≤ -2.

Front

What is the solution to the inequality -4x + 14 ≤ 54?

Back

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

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 is the solution to the inequality 4(2a + 3) < 3(a - 1)?

Back

Distribute: 8a + 12 < 3a - 3. Subtract 3a: 5a + 12 < -3. Subtract 12: 5a < -15. Divide by 5: a < -3.

Front

What does the solution a < -3 mean in context?

Back

It means that a can be any number less than -3.

Front

What is the first step in solving a multi-step inequality?

Back

The first step is to simplify both sides of the inequality, if necessary, by combining like terms or distributing.