4.7 Writing 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 often involves addition or subtraction followed by multiplication or division.

Front

How do you write an inequality for a situation where a total amount cannot exceed a certain limit?

Back

You express the total amount as a sum or difference and set it less than or equal to the limit. For example, if spending cannot exceed $60, you write: total ≤ 60.

Front

In the inequality 22 + 8x ≤ 60, what does x represent?

Back

In this inequality, x represents the number of t-shirts Debbie can buy.

Front

What does the symbol '≤' mean in an inequality?

Back

The symbol '≤' means 'less than or equal to', indicating that the value on the left can be less than or equal to the value on the right.

Front

How do you solve the inequality 71 - 3.5x < 50 for x?

Back

First, subtract 71 from both sides: -3.5x < -21. Then, divide by -3.5 (remember to flip the inequality): x > 6.

Front

What is the first step in writing an inequality for a word problem?

Back

Identify the variable and what it represents in the context of the problem.

Front

In the inequality 668 + 7n > 2000, what does n represent?

Back

In this inequality, n represents the average number of cans collected each day over the final 7 days.

Front

What is the purpose of using inequalities in real-life situations?

Back

Inequalities help to express limits, constraints, or conditions that must be met in various scenarios, such as budgeting or resource allocation.

Front

How do you interpret the inequality 2 + 3n ≤ 14?

Back

This inequality means that the total cost of a soda ($2) plus the cost of n nachos (each costing $3) must be less than or equal to $14.

Front

What is the difference between an equation and an inequality?

Back

An equation states that two expressions are equal, while an inequality shows that one expression is greater than, less than, or not equal to another.