To solve the equation [tex]\(\frac{5}{2}x - 7 = \frac{3}{4}x + 14\)[/tex], follow these detailed steps:
1. Eliminate the fractions by multiplying both sides of the equation by 4 to make the coefficients easier to work with.
[tex]\[
4 \left(\frac{5}{2}x - 7\right) = 4 \left(\frac{3}{4}x + 14\right)
\][/tex]
Simplify this to:
[tex]\[
4 \cdot \frac{5}{2}x - 4 \cdot 7 = 4 \cdot \frac{3}{4}x + 4 \cdot 14
\][/tex]
[tex]\[
2 \cdot 5x - 28 = 3x + 56
\][/tex]
[tex]\[
10x - 28 = 3x + 56
\][/tex]
2. Move the terms involving [tex]\(x\)[/tex] to one side by subtracting [tex]\(3x\)[/tex] from both sides of the equation:
[tex]\[
10x - 3x - 28 = 3x - 3x + 56
\][/tex]
[tex]\[
7x - 28 = 56
\][/tex]
3. Isolate [tex]\(x\)[/tex] by adding 28 to both sides:
[tex]\[
7x - 28 + 28 = 56 + 28
\][/tex]
[tex]\[
7x = 84
\][/tex]
4. Solve for [tex]\(x\)[/tex] by dividing both sides by 7:
[tex]\[
x = \frac{84}{7}
\][/tex]
[tex]\[
x = 12
\][/tex]
Therefore, the solution to the equation [tex]\(\frac{5}{2}x - 7 = \frac{3}{4}x + 14\)[/tex] is [tex]\(x = 12\)[/tex].
So, the correct answer is:
D. [tex]\( x = 12 \)[/tex]
