Two-step inequalities

Front

What is a two-step inequality?

Back

A two-step inequality is an inequality that requires two operations to isolate the variable. It typically involves addition or subtraction followed by multiplication or division.

Front

How do you solve the inequality 22 < 6c + 4?

Back

Subtract 4 from both sides: 22 - 4 < 6c, which simplifies to 18 < 6c. Then divide by 6: 3 < c or c > 3.

Front

What does the solution x ≥ -7 represent in a number line?

Back

It represents all numbers greater than or equal to -7, including -7 itself, extending to the right on the number line.

Front

How do you solve the inequality -3x - 4 < 5?

Back

Add 4 to both sides: -3x < 9. Then divide by -3 (remember to flip the inequality): x > -3.

Front

What is the solution to the inequality 3w - 2 < -17?

Back

Add 2 to both sides: 3w < -15. Then divide by 3: w < -5.

Front

What does the inequality 2 + 3x ≤ 20 mean?

Back

It means that when you add 2 to three times a number x, the result is less than or equal to 20.

Front

How do you isolate the variable in the inequality 2x + 6 ≥ -8?

Back

Subtract 6 from both sides: 2x ≥ -14. Then divide by 2: x ≥ -7.

Front

What is the first step in solving the inequality 22 < 6c + 4?

Back

The first step is to subtract 4 from both sides to simplify the inequality.

Front

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

Back

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

Front

What is the solution set for the inequality x < -3?

Back

The solution set includes all numbers less than -3, extending to the left on the number line.