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 like 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.

Tags

CCSS.6.EE.B.8

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 -4x + 14 ≤ 54?

Back

Subtract 14 from both sides: -4x ≤ 40. Divide by -4 (flip the inequality): x ≥ -10.

Tags

CCSS.6.EE.B.8

Front

What is the solution to the inequality p ≥ 20?

Back

It means p can be any number greater than or equal to 20.

Tags

CCSS.6.EE.B.8

Front

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

Back

The first step is to simplify the inequality by distributing and combining like terms.

Front

What happens to the inequality sign when you multiply or divide by a negative number?

Back

The inequality sign flips when you multiply or divide both sides by a negative number.

Tags

CCSS.6.EE.B.8

Front

What is the solution to the inequality 3x - 5 > 1?

Back

Add 5 to both sides: 3x > 6. Then divide by 3: x > 2.

Tags

CCSS.7.EE.B.4B