Sure, let's solve the equation [tex]\(4 = 8x - 10y\)[/tex] for [tex]\(x\)[/tex].
We start with the given equation:
[tex]\[ 4 = 8x - 10y \][/tex]
Our goal is to isolate [tex]\(x\)[/tex] on one side of the equation. Here are the steps to do so:
1. Add [tex]\(10y\)[/tex] to both sides of the equation:
[tex]\[
4 + 10y = 8x
\][/tex]
2. Divide both sides of the equation by 8 to solve for [tex]\(x\)[/tex]:
[tex]\[
x = \frac{4 + 10y}{8}
\][/tex]
3. Simplify the fraction if possible:
[tex]\[
x = \frac{4 + 10y}{8}
\][/tex]
The fraction can be simplified further by dividing both the numerator and the denominator by their greatest common divisor, which is 2:
[tex]\[
x = \frac{4/2 + 10y/2}{8/2} = \frac{2 + 5y}{4}
\][/tex]
So the solution to the equation [tex]\(4 = 8x - 10y\)[/tex] in terms of [tex]\(x\)[/tex] is:
[tex]\[
x = \frac{2 + 5y}{4}
\][/tex]
