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.
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.
