FA 8-2: Two-Step Inequalities Word Problems

Front

What is a two-step inequality?

Back

A two-step inequality is an inequality that requires two operations to isolate the variable. It often involves addition or subtraction followed by multiplication or division.

Front

How do you solve the inequality u/7 – 1 ≤ 1?

Back

Add 1 to both sides: u/7 ≤ 2. Then multiply both sides by 7: u ≤ 14.

Front

What does the inequality 15 + 6x ≤ 100 represent in a word problem?

Back

It represents a situation where Lazer Zone charges $15 plus $6 per person, and Andrea has a maximum of $100 to spend.

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 is the solution to the inequality 7n - 1 > 76?

Back

Add 1 to both sides: 7n > 77. Then divide by 7: n > 11.

Front

What inequality represents the highest possible price of the skirt if Mrs. Scott spends no more than $120?

Back

The inequality is 3x + 20 ≤ 120, where x is the price of the skirt.

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 difference between a two-step equation and a two-step inequality?

Back

A two-step equation has an equal sign, while a two-step inequality has an inequality sign (like <, >, ≤, or ≥).

Front

How do you graph the solution of an inequality?

Back

You plot the solution on a number line, using an open circle for < or > and a closed circle for ≤ or ≥, then shade the appropriate direction.

Front

What does it mean if an inequality is written as x < 5?

Back

It means that x can be any number less than 5.