To solve the equation [tex]\(\frac{1}{2}(x + 9) = \frac{7}{8} x\)[/tex], we need to isolate [tex]\(x\)[/tex]. Here are the steps to do that:
1. Start with the given equation:
[tex]\[
\frac{1}{2}(x + 9) = \frac{7}{8} x
\][/tex]
2. To eliminate the fraction on the left side, multiply both sides of the equation by 2:
[tex]\[
2 \cdot \frac{1}{2}(x + 9) = 2 \cdot \frac{7}{8} x
\][/tex]
which simplifies to:
[tex]\[
x + 9 = \frac{7}{4} x
\][/tex]
3. Next, we want to isolate [tex]\(x\)[/tex] on one side of the equation. Subtract [tex]\(x\)[/tex] from both sides to gather all [tex]\(x\)[/tex]-terms on the right side:
[tex]\[
9 = \frac{7}{4} x - x
\][/tex]
4. Subtract [tex]\(x\)[/tex] from [tex]\(\frac{7}{4} x\)[/tex]:
[tex]\[
\frac{7}{4} x - x = \frac{7}{4} x - \frac{4}{4} x = \frac{3}{4} x
\][/tex]
So, the equation now looks like:
[tex]\[
9 = \frac{3}{4} x
\][/tex]
5. To solve for [tex]\(x\)[/tex], multiply both sides of the equation by the reciprocal of [tex]\(\frac{3}{4}\)[/tex], which is [tex]\(\frac{4}{3}\)[/tex]:
[tex]\[
x = 9 \cdot \frac{4}{3}
\][/tex]
Simplifying this:
[tex]\[
x = 12
\][/tex]
Therefore, the solution to the equation is:
[tex]\[
x = 1.75
\][/tex]
