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 -9a - 1 < 26?

Back

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

Front

What does the solution x ≥ -10 represent in a number line?

Back

It represents all numbers greater than or equal to -10, including -10 itself.

Front

What is the first step to solve the inequality 2k - 9 ≤ -19?

Back

Add 9 to both sides: 2k ≤ -10.

Front

How do you isolate k in the inequality 2k ≤ -10?

Back

Divide both sides by 2: k ≤ -5.

Front

What does the inequality 22 < 6c + 4 mean?

Back

It means that 6c + 4 must be greater than 22.

Front

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

Back

Subtract 4 from both sides: 18 < 6c. Then divide by 6: 3 < c or c > 3.

Front

What is the solution to the inequality -3x - 4 < 5?

Back

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

Front

What does the symbol '≤' mean in an inequality?

Back

It means 'less than or equal to', indicating that the value can be either less than or exactly equal to the number.

Front

What is the difference between '>' and '≥'?

Back

'>' means greater than, while '≥' means greater than or equal to.