step 1 To solve for x, we're going to add x plus x over 4. So we changed denominator to common denomina

Question

$ \quad \frac{x}{2}+7=13-\frac{x}{4}$

Name: Problem 79, Chapter 3: Introductory Algebra for College Students
Uploaded: 2021-02-03T16:36:47-08:00
Duration: 41 s
Channel: Michelle Nguyen
Description: (x)/(2)+7=13-(x)/(4)

   $ \quad \frac{x}{2}+7=13-\frac{x}{4}$

Introductory Algebra for College Students

Robert Blitzer 6th Edition

Chapter 3, Problem 79

Instant Answer

Solved by Expert Michelle Nguyen

02/03/2021

Step 1

To do this, we multiply every term by 4 to get a common denominator: \[4 \cdot \frac{x}{2} + 4 \cdot 7 = 4 \cdot 13 - 4 \cdot \frac{x}{4}\] This simplifies to: \[2x + 28 = 52 - x\] Show more…

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$ \quad \frac{x}{2}+7=13-\frac{x}{4}$

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Key Concepts

Linear Equations

A linear equation is an algebraic equation in which each term is either a constant or a product of a constant and a variable raised to the first power. They represent relationships with a constant rate of change and are fundamental in modeling real-world situations and solving problems involving unknown quantities.

Clearing Fractions

Clearing fractions involves multiplying every term in the equation by the least common denominator to eliminate fractions. This simplification makes it easier to manipulate and solve the equation because it converts fractional coefficients into whole numbers.

Isolating the Variable

Isolating the variable is a method used to solve equations by performing inverse operations to get the unknown variable on one side of the equation. This step-by-step process typically involves adding, subtracting, multiplying, or dividing both sides of the equation to simplify and ultimately determine the value of the variable.

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