College

Solve the following equation for [tex]x[/tex].

[tex]\frac{1}{4} x - 7 = \frac{3}{8} x - 5[/tex]

A. 12
B. 16
C. -48
D. -16

Answer :

Let's solve the equation [tex]\(\frac{1}{4}x - 7 = \frac{3}{8}x - 5\)[/tex] step-by-step to find the value of [tex]\(x\)[/tex].

1. Eliminate fractions by finding a common denominator. Here, the least common multiple of 4 and 8 is 8. Multiply every term by 8 to clear the fractions:

[tex]\[
8 \left(\frac{1}{4}x\right) - 8(7) = 8 \left(\frac{3}{8}x\right) - 8(5)
\][/tex]

Simplify each term:

[tex]\[
2x - 56 = 3x - 40
\][/tex]

2. Move all the [tex]\(x\)[/tex]-terms to one side. We'll subtract [tex]\(2x\)[/tex] from both sides:

[tex]\[
2x - 2x - 56 = 3x - 2x - 40
\][/tex]

Simplify:

[tex]\[
-56 = x - 40
\][/tex]

3. Isolate [tex]\(x\)[/tex] by adding 40 to both sides:

[tex]\[
-56 + 40 = x - 40 + 40
\][/tex]

Simplify:

[tex]\[
-16 = x
\][/tex]

Therefore, the solution to the equation is [tex]\(x = -16\)[/tex]. The correct answer is option D.