Multistep inequalities

Front

What is a multistep inequality?

Back

A multistep 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 17x − 4 > 30?

Back

Add 4 to both sides: 17x > 34. Then divide by 17: x > 2.

Front

What does the solution x > 2 mean in a real-world context?

Back

It means that x can take any value greater than 2, which could represent a quantity or measurement that must exceed 2.

Front

What is the first step to solve the inequality 4(5x + 2) ≤ 28?

Back

Distribute 4: 20x + 8 ≤ 28.

Front

How do you isolate x in the inequality 20x + 8 ≤ 28?

Back

Subtract 8 from both sides: 20x ≤ 20, then divide by 20: x ≤ 1.

Front

What does the solution x ≤ 1 indicate?

Back

It indicates that x can be any value less than or equal to 1.

Front

How do you solve the inequality x − 14 < 22?

Back

Add 14 to both sides: x < 36.

Front

What is the solution to the inequality 2x − 33 < 15?

Back

Add 33 to both sides: 2x < 48, then divide by 2: x < 24.

Front

What does the solution x < 24 signify?

Back

It signifies that x can take any value less than 24.

Front

How do you solve the inequality -2(x + 2) < 14?

Back

Distribute -2: -2x - 4 < 14. Then add 4: -2x < 18, and divide by -2 (remember to flip the inequality): x > -9.