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Chapter 4: Problem 16

Solve the equations. Write the answers as fractions or whole numbers. $$r-\frac{4}{7}=-1$$

Short Answer

Expert verified
\(-\frac{3}{7}\)

Step by step solution

01

Isolate the variable

To isolate the variable, add \(\frac{4}{7}\) to both sides of the equation. The equation becomes: \[r = -1 + \frac{4}{7}\]
02

Calculate the right-hand side

Convert \(-1\) to a fraction with the same denominator to combine the fractions: \(-1 = \frac{-7}{7}\). Now the equation is \[r = \frac{-7}{7} + \frac{4}{7}\]
03

Combine the fractions

Combine the fractions by adding the numerators: \[r = \frac{-7+4}{7} = \frac{-3}{7}\]
04

Solution

The value of \(r\) that satisfies the equation is \(\frac{-3}{7}\).

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Key Concepts

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

Fractions
Fractions are numbers that represent a part of a whole. They consist of a numerator and a denominator. The numerator is the top number that indicates how many parts we have. The denominator is the bottom number that shows how many equal parts the whole is divided into. When solving equations involving fractions, it's crucial to manipulate them correctly to maintain the equation's balance. If the denominators are different, you may need to find a common denominator before performing operations like addition or subtraction. In our example, we combine fractions by ensuring they have the same denominator.
Isolating the Variable
Isolating the variable means getting the variable by itself on one side of the equation. This is the primary goal when solving equations. To achieve this, we perform operations that will

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Most popular questions from this chapter

Simplify the expression. $$-\frac{6 a c^{2}}{12 a c^{4}}$$

Jonathan and Jared both sold candy bars for a fundraiser. Jonathan sold 25 of his 35 candy bars, and Jared sold 24 of his 28 candy bars. a. What fractional part of his total number of candy bars did each person sell? b. Which person sold the greater fractional part?

Convert the improper fraction to a mixed number. $$\frac{13}{7}$$

Write three fractions equivalent to \(\frac{1}{3}\)

Simplify to lowest terms by first reducing the powers of 10. $$\frac{120}{160}$$
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