Sure, let's go through the steps in detail to solve the equation [tex]\(\frac{1}{2}(x + 9) = \frac{7}{8}x\)[/tex].
1. We begin with the equation [tex]\(\frac{1}{2}(x + 9) = \frac{7}{8}x\)[/tex].
2. To eliminate the fraction on the left side of the equation, we divide both sides of the equation by [tex]\(\frac{1}{2}\)[/tex]:
[tex]\[
\left(\frac{1}{2}(x + 9)\right) \div \frac{1}{2} = \left(\frac{7}{8}x\right) \div \frac{1}{2}
\][/tex]
3. Dividing by [tex]\(\frac{1}{2}\)[/tex] is the same as multiplying by 2:
[tex]\[
(x + 9) = \frac{7}{8}x \times \frac{2}{1}
\][/tex]
4. Simplify the right-hand side by multiplying the fractions:
[tex]\[
x + 9 = \frac{7 \cdot 2}{8 \cdot 1}x = \frac{14}{8}x
\][/tex]
5. Further simplify the fraction [tex]\(\frac{14}{8}\)[/tex]:
[tex]\[
x + 9 = \frac{7}{4}x
\][/tex]
Therefore, the new equation after dividing both sides by [tex]\(\frac{1}{2}\)[/tex] and simplifying the fractions is:
[tex]\[
x + 9 = \frac{7}{4}x
\][/tex]
