Problem 139 - Algebra and Trigonometry

Question

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

Step-by-Step Solution

Answer

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

Step 1: 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.

Step 2: 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 \( \frac{x+3}{4} = \frac{4x-5}{12} \).

Step 3: Cross-Multiply

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

Step 4: 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.

Step 5: Solve for x

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