Question

Solve each equation. Leave your answer as a fraction if it is not an integer value. $\frac{5}{14} x+\frac{3}{7}=\frac{1}{7} x-\frac{3}{2}$

Name: Problem 102, Chapter 2: Intermediate Algebra for College Students
Uploaded: 2022-04-04T02:47:14-08:00
Duration: 17 s
Channel: Erika Bustos
Description: Solve each equation. Leave your answer as a fraction if it is not an integer value. (5)/(14) x+(3)/(7)=(1)/(7) x-(3)/(2)

   Solve each equation. Leave your answer as a fraction if it is not an integer value. $\frac{5}{14} x+\frac{3}{7}=\frac{1}{7} x-\frac{3}{2}$

Intermediate Algebra for College Students

Allen R. Angel;… 10th Edition

Chapter 2, Problem 102

Instant Answer

Solved by Expert Erika Bustos

04/04/2022

Step 1

In this case, the common denominator is 14. Show more…

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Solve each equation. Leave your answer as a fraction if it is not an integer value. $\frac{5}{14} x+\frac{3}{7}=\frac{1}{7} x-\frac{3}{2}$

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Key Concepts

Isolating the Variable

Isolating the variable involves applying algebraic operations, such as addition, subtraction, multiplication, or division, consistently to both sides of an equation. This technique is central to solving any equation, as it allows one to express the unknown variable explicitly in terms of known quantities.

Linear Equations

A linear equation is an equation of the first degree, meaning the variable is raised only to the power of one. Solving a linear equation typically involves isolating the variable on one side of the equation by performing equivalent operations on both sides.

Fraction Arithmetic

When equations involve fractions, it is important to manage fractional expressions by finding common denominators or multiplying through by the least common denominator to eliminate the fractions. This process simplifies the equation and makes the algebraic manipulation more straightforward.

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