Let's solve the equation [tex]\( \frac{x + 8}{3} = \frac{3x - 2}{8} \)[/tex] using cross-multiplication.
### Step-by-step Solution:
1. Set up the cross-multiplication:
The initial equation is:
[tex]\[
\frac{x + 8}{3} = \frac{3x - 2}{8}
\][/tex]
To eliminate the fractions, we multiply both sides of the equation by the denominators on each side, resulting in:
[tex]\[
(x + 8) \cdot 8 = (3x - 2) \cdot 3
\][/tex]
2. Multiply out both sides:
[tex]\[
8(x + 8) = 3(3x - 2)
\][/tex]
Simplifying both sides:
[tex]\[
8x + 64 = 9x - 6
\][/tex]
3. Move the terms involving [tex]\(x\)[/tex] to one side:
To isolate [tex]\(x\)[/tex], we can subtract [tex]\(8x\)[/tex] from both sides:
[tex]\[
64 = 9x - 8x - 6
\][/tex]
Simplifying further:
[tex]\[
64 = x - 6
\][/tex]
4. Isolate [tex]\(x\)[/tex]:
Add 6 to both sides of the equation to solve for [tex]\(x\)[/tex]:
[tex]\[
64 + 6 = x
\][/tex]
Simplifying the right-hand side:
[tex]\[
70 = x
\][/tex]
### Final Answer:
[tex]\[
x = 70
\][/tex]
