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. It often involves addition or subtraction followed by multiplication or division.

Front

How do you represent a situation with an inequality?

Back

You identify the quantities involved, determine the relationship (greater than, less than, etc.), and express it using an inequality symbol.

Front

What does the inequality 5x + 60 ≥ 200 represent?

Back

It represents the situation where Evelyn's total savings (current savings plus weekly allowance times weeks) is at least $200.

Front

What is the first step to solve the inequality 5x + 60 ≥ 200?

Back

Subtract 60 from both sides to isolate the term with the variable: 5x ≥ 140.

Front

What does the inequality 15 + 6x ≤ 100 represent in the context of Andrea's laser tag invitation?

Back

It represents the total cost of inviting x people to laser tag, which must be less than or equal to $100.

Front

How do you solve the inequality 15 + 6x ≤ 100 for x?

Back

Subtract 15 from both sides to get 6x ≤ 85, then divide by 6 to find x ≤ 14.17.

Front

What is the significance of the inequality x < 15 in the taxi problem?

Back

It indicates that the maximum number of miles you can ride in the taxi is less than 15 miles without exceeding $14.

Front

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

Back

It represents the total cost of hiring a DJ and an assistant, which must be less than $600.

Front

How do you find the maximum hours the DJ can play using the inequality 125x + 55 < 600?

Back

Subtract 55 from both sides to get 125x < 545, then divide by 125 to find x < 4.36 hours.

Front

What is the maximum number of cookie batches Calvin can make with 10 cups of sugar?

Back

The inequality 1.5x - 2 ≤ 10 represents the maximum batches, leading to x ≤ 8 batches after solving.