2-Step Inequalities

Front

What is a 2-step inequality?

Back

A 2-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 7k - 2 ≥ -9?

Back

Add 2 to both sides: 7k ≥ -7. Then divide by 7: k ≥ -1.

Front

What does the solution k ≥ -1 represent on a number line?

Back

It represents all numbers greater than or equal to -1, including -1 itself.

Front

How do you solve the inequality 16 - 4a > 8?

Back

Subtract 16 from both sides: -4a > -8. Then divide by -4 (remember to flip the inequality): a < 2.

Front

What does the solution a < 2 indicate?

Back

It indicates that a can be any number less than 2.

Front

How do you solve the inequality -2x - 8 ≤ 18?

Back

Add 8 to both sides: -2x ≤ 26. Then divide by -2 (flip the inequality): x ≥ -13.

Front

What does the solution x ≥ -13 mean?

Back

It means x can be any number greater than or equal to -13.

Front

How do you solve the inequality 6t + 4 ≤ -2?

Back

Subtract 4 from both sides: 6t ≤ -6. Then divide by 6: t ≤ -1.

Front

What does the solution t ≤ -1 represent?

Back

It represents all numbers less than or equal to -1.

Front

How do you solve the inequality x/-4 + 2 > 7?

Back

Subtract 2 from both sides: x/-4 > 5. Then multiply by -4 (flip the inequality): x < -20.