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Chapter 1: Problem 139

Will help you prepare for the material covered in the next section. Solve: \(\frac{x+3}{4}=\frac{x-2}{3}+\frac{1}{4}\)

Short Answer

Expert verified
The solution to the equation is \(x = 14\).

Step by step solution

01

Simplify the equation

Begin by simplifying the equation wherever possible. In this case, we could combine the fractions on the right side of the equation by finding a common denominator, which is 12 in this case.
02

Simplify the right side of the equation

By simplifying, the equation becomes \( \frac{x+3}{4} = \frac{4x-8+3}{12} \). Then further simplify to \( \frac{x+3}{4} = \frac{4x-5}{12} \).
03

Cross-Multiply

To eliminate the fraction, we do a cross-multiplication which results in 12(x+3) = 4(4x-5).
04

Expand Both Sides and Simplify

Expanding gives: 12x + 36 = 16x - 20. Next, we rearrange the terms to isolate x. By subtracting 12x from both sides, we get: 36 = 4x - 20.
05

Solve for x

Finally, by adding 20 to both sides and dividing by 4, the value of \(x\) is found to be 14.

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