To solve the equation [tex]\(\frac{7}{x-4} = \frac{3}{5}\)[/tex], we will proceed with the following steps:
1. Cross-multiply the fractions to eliminate the denominators:
[tex]\[
\frac{7}{x-4} = \frac{3}{5}
\][/tex]
Cross-multiplying gives us:
[tex]\[
7 \cdot 5 = 3 \cdot (x - 4)
\][/tex]
2. Simplify the equation:
[tex]\[
35 = 3(x - 4)
\][/tex]
3. Distribute the 3 on the right-hand side:
[tex]\[
35 = 3x - 12
\][/tex]
4. Isolate the variable [tex]\(x\)[/tex]:
Add 12 to both sides of the equation to get rid of the constant term on the right-hand side.
[tex]\[
35 + 12 = 3x - 12 + 12
\][/tex]
Simplifying this, we have:
[tex]\[
47 = 3x
\][/tex]
5. Solve for [tex]\(x\)[/tex]:
Divide both sides of the equation by 3 to isolate [tex]\(x\)[/tex].
[tex]\[
x = \frac{47}{3}
\][/tex]
Therefore, the solution to the equation [tex]\(\frac{7}{x - 4} = \frac{3}{5}\)[/tex] is:
[tex]\[
x = \frac{47}{3}
\][/tex]
