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Chapter 2: Problem 20

Translate to an inequality. The cost of gasoline was at most \(\$ 4\) per gallon.

Short Answer

Expert verified
x \leq 4

Step by step solution

01

Define the Variable

Let the cost of gasoline per gallon be denoted by the variable \( x \).
02

Understand the Phrase

The phrase 'at most' means that the value can be less than or equal to a specific amount.
03

Set up the Inequality

Since the cost of gasoline was at most \( \$4 \) per gallon, the inequality would be written as \( x \leq 4 \).

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

defining variables
When working with inequalities in algebra, one of the first steps is to define the variables. Variables are symbols, in this case, letters that stand for unknown values. For example, let's consider the cost of gasoline. We don't know the exact cost, so we use a variable to represent it. In our problem, we used the variable \( x \) to represent the cost per gallon of gasoline. Defining variables clearly is crucial because they allow us to write mathematical expressions and solve problems step by step.
interpreting phrases
Understanding the meaning of specific phrases is key to setting up inequalities correctly. In our example, we encountered the phrase 'at most.' This phrase means that the value can be equal to or less than a certain number. So, if the gasoline cost is 'at most \( \$4 \)', it means the cost per gallon can be \( \$4 \) or any amount less than \( \$4 \). It's important to interpret these phrases accurately because they dictate how you set up your inequality. Other similar phrases you might encounter include 'at least,' 'more than,' and 'less than.' Each of these indicates a different kind of mathematical relationship.
setting up inequalities
After defining your variables and interpreting the phrases, the next step is setting up the inequality. Based on our problem, we know the cost, represented by \( x \), should be no more than \( \$4 \) per gallon. We translate this into a mathematical inequality: \( x \leq 4 \).
This notation tells us that \( x \) can be any number less than or equal to 4.
Setting up inequalities correctly is crucial as it provides the mathematical foundation needed to find solutions and make decisions based on them.

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Most popular questions from this chapter

Use an inequality and the five-step process to solve each problem. An unconditional acceptance into the Master of Business Administration (MBA) program at Arkansas State University will be given to students whose GMAT score plus 200 times the undergraduate grade point average is at least \(950 .\) Chloe's GMAT score was \(500 .\) What must her grade point average be in order to be unconditionally accepted into the program?

Use an inequality and the five-step process to solve each problem. Most insurance companies will replace a vehicle if an estimated repair exceeds \(80 \%\) of the "blue-book" value of the vehicle. Michelle's insurance company paid \(\$ 8500\) for repairs to her Subaru after an accident. What can be concluded about the blue-book value of the car?

To prepare for Section 2.5, review translating to algebraic expressions and equations. Translate to an algebraic expression or equation. Erin is returning a tent that she bought during a \(25 \%\) off storewide sale that has ended. She is offered store credit for \(125 \%\) of what she paid (not to be used on sale items). Is this fair to Erin? Why or why not?

Match the sentence with one of the following: $$ a

The sum of two consecutive odd integers is less than \(100 .\) What is the largest pair of such integers?
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