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, typically involving addition or subtraction followed by multiplication or division.

Front

How do you solve the inequality x/3 < 2?

Back

Multiply both sides by 3: x < 6.

Front

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

Back

The inequality sign flips direction.

Front

Solve for k in the inequality 2k - 9 ≤ -19.

Back

Add 9 to both sides: 2k ≤ -10; then divide by 2: k ≤ -5.

Front

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

Back

Subtract 14 from both sides: -4x ≤ 40; then divide by -4 (flip the sign): x ≥ -10.

Front

What does the inequality b ≤ -2 represent on a number line?

Back

It represents all numbers less than or equal to -2, including -2 itself.

Front

What is the first step in solving the inequality -3x ≥ 12?

Back

Divide both sides by -3 (remember to flip the inequality sign): x ≤ -4.

Front

What does it mean to 'isolate the variable' in an inequality?

Back

It means to get the variable by itself on one side of the inequality.

Front

If you have the inequality 5x + 3 < 18, what is the first step to solve it?

Back

Subtract 3 from both sides: 5x < 15.

Front

What is the solution to the inequality 2x - 4 > 10?

Back

Add 4 to both sides: 2x > 14; then divide by 2: x > 7.