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 6t + 4 ≤ -2?

Back

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

Front

What does the inequality -12x + 1 > -47 represent?

Back

To solve, subtract 1 from both sides: -12x > -48. Then divide by -12 (remember to flip the inequality): x < 4.

Front

What is the solution to the inequality 7k - 2 ≥ -9?

Back

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

Front

What does the inequality 15 + 6x ≤ 100 represent in a real-world context?

Back

It represents the situation where Lazer Zone charges $15 plus $6 per person, and Andrea wants to know how many people she can invite if she has a maximum of $100.

Front

How do you represent the goal of Casey's dog losing weight with an inequality?

Back

The inequality is 106 - 4x ≤ 70, where x is the number of weeks.

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 a constant from both sides.

Front

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

Back

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

Front

What is the solution set for the inequality x < 4?

Back

The solution set includes all real numbers less than 4.

Front

How can you check if your solution to an inequality is correct?

Back

You can check by substituting a value from the solution set back into the original inequality to see if it holds true.