2 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 -4x + 5 ≤ 29?

Back

Subtract 5 from both sides: -4x ≤ 24. Then divide by -4 (remember to flip the inequality): x ≥ -6.

Front

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

Back

The inequality symbol flips direction.

Front

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

Back

It represents a 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

Solve for t: 6t + 4 ≤ -2

Back

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

Front

Solve for k: 7k - 2 ≥ -9

Back

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

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.

Front

What is the solution set for the inequality x + 3 > 5?

Back

x > 2.

Front

How do you check your solution for an inequality?

Back

Substitute the solution back into the original inequality to see if it holds true.

Front

What does it mean if an inequality has no solution?

Back

It means there are no values for the variable that can satisfy the inequality.