Day 9 Two-Step Inequalities Word Problems - Math 7

Front

What is a two-step inequality?

Back

A two-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 represent a situation where you need at least a certain amount of money?

Back

You can represent this situation with an inequality using the 'greater than or equal to' symbol (≥). For example, if you need at least $240, you would write: x ≥ 240.

Front

What does the inequality 14x + 30 ≥ 240 represent?

Back

It represents the situation where Aaron earns $14 for each car washed (x) and has already saved $30, needing at least $240 to buy headphones.

Front

What is the first step to solve the inequality 14x + 30 ≥ 240?

Back

The first step is to subtract 30 from both sides of the inequality: 14x ≥ 210.

Front

What does the inequality 125x + 55 < 600 represent?

Back

It represents the maximum amount of hours (x) the DJ can play while keeping the total cost under $600.

Front

How do you solve the inequality 125x + 55 < 600?

Back

First, subtract 55 from both sides: 125x < 545, then divide by 125: x < 4.36.

Front

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

Back

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

Front

If you have $14 and a taxi charges $5 plus $0.60 per mile, how do you set up the inequality?

Back

You set up the inequality as: 5 + 0.60x ≤ 14, where x is the number of miles.

Front

What is the maximum number of miles you can ride in the taxi without exceeding $14?

Back

You can ride a maximum of 15 miles, as the inequality 0.60x ≤ 9 (after subtracting $5) gives x ≤ 15.

Front

What does the term 'isolating the variable' mean in solving inequalities?

Back

Isolating the variable means manipulating the inequality to get the variable alone on one side, making it easier to find its value.