3.3 Solving 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 -9x + 7 ≥ 25?

Back

Subtract 7 from both sides: -9x ≥ 18. Then divide by -9 (remember to flip the inequality): x ≤ -2.

Front

What does the solution x < 3 represent on a number line?

Back

It represents all numbers to the left of 3, not including 3 itself.

Front

Which inequality results in the solution x < 3?

Back

4x - 8 < 4.

Front

How do you solve the inequality -9a - 1 < 26?

Back

Add 1 to both sides: -9a < 27. Then divide by -9 (flip the inequality): a > -3.

Front

What is the solution to the inequality a ≥ -104?

Back

It includes all numbers greater than or equal to -104.

Front

What does the inequality 11 ≤ a mean?

Back

It means that a is greater than or equal to 11.

Front

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

Back

The first step is usually to isolate the term with the variable by adding or subtracting.

Front

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

Back

The inequality sign flips direction.

Front

How do you graph the inequality x ≤ -2?

Back

Draw a number line, place a closed circle on -2, and shade to the left.