Question

Solve each equation, and check the solution. See Examples $1-3 .$ 27. $\frac{x}{2}-5=\frac{x}{7}$

Name: Problem 27, Chapter 2: Beginning and Intermediate Algebra
Uploaded: 2022-02-07T04:06:02-08:00
Duration: 1 min 17 s
Channel: Nick Johnson
Description: Solve each equation, and check the solution. See Examples 1-3 . 27. (x)/(2)-5=(x)/(7)

   Solve each equation, and check the 

solution. See Examples $1-3 .$
27. $\frac{x}{2}-5=\frac{x}{7}$

Beginning and Intermediate Algebra

Margaret L. Lial,… 7th Edition

Chapter 2, Problem 27

Instant Answer

Solved by Expert Nick Johnson

02/07/2022

Step 1

Multiply both sides by 14 (LCM of 2 and 7): 14*(x/2 - 5) = 14*(x/7) → 7x - 70 = 2x. Subtract 2x: 5x - 70 = 0 → 5x = 70 → x = 14. Show more…

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Solve each equation, and check the solution. See Examples $1-3 .$ 27. $\frac{x}{2}-5=\frac{x}{7}$

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Key Concepts

Verification of Solutions

Once a solution has been found for an equation, it is important to check the solution by substituting it back into the original equation. Verification ensures that no mistakes were made during the solving process and that the solution truly satisfies the given equation.

Clearing Fractions

When an equation contains fractions, a common technique is to eliminate the fractions by multiplying every term in the equation by a common denominator. This process simplifies the equation to a form without fractions, making subsequent algebraic manipulation simpler.

Linear Equations

A linear equation is an algebraic equation in which each term is either a constant or the product of a constant and a single variable. In this context, solving a linear equation involves finding the value of the variable that makes the equation true, typically by isolating the variable on one side of the equation.

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