Let's solve the equation step by step:
1. Original Equation:
[tex]\[
0.05x + 0.20(8) = 0.10(x + 8)
\][/tex]
2. Simplify the constant term on the left side:
[tex]\[
0.20 \times 8 = 1.6
\][/tex]
So, the equation becomes:
[tex]\[
0.05x + 1.6 = 0.10(x + 8)
\][/tex]
3. Expand the right side of the equation:
[tex]\[
0.10(x + 8) = 0.10x + 0.80
\][/tex]
So, now the equation is:
[tex]\[
0.05x + 1.6 = 0.10x + 0.80
\][/tex]
4. Move all terms involving [tex]\(x\)[/tex] to one side and constants to the other:
Subtract [tex]\(0.05x\)[/tex] from both sides:
[tex]\[
0.05x + 1.6 - 0.05x = 0.10x + 0.80 - 0.05x
\][/tex]
Simplifying, we get:
[tex]\[
1.6 = 0.05x + 0.80
\][/tex]
5. Subtract 0.80 from both sides to isolate the term with [tex]\(x\)[/tex]:
[tex]\[
1.6 - 0.80 = 0.05x + 0.80 - 0.80
\][/tex]
Simplifying, we get:
[tex]\[
0.80 = 0.05x
\][/tex]
6. Solve for [tex]\(x\)[/tex] by dividing both sides by 0.05:
[tex]\[
x = \frac{0.80}{0.05}
\][/tex]
7. Calculate the value of [tex]\(x\)[/tex]:
[tex]\[
x = 16.0
\][/tex]
So, the solution to the equation is:
[tex]\[
x = 16.0
\][/tex]
