To solve the equation [tex]\(a + c = \frac{b - a}{5}\)[/tex] for the variable [tex]\(a\)[/tex], follow these steps:
1. Isolate the fraction on one side:
Start by getting rid of the fraction. Multiply both sides of the equation by 5 to clear the denominator:
[tex]\[
5(a + c) = b - a
\][/tex]
2. Distribute on left side:
Distribute 5 to both terms within the parentheses:
[tex]\[
5a + 5c = b - a
\][/tex]
3. Rearrange the terms:
Move all terms involving [tex]\(a\)[/tex] to one side of the equation and constants to the other side. Add [tex]\(a\)[/tex] to both sides:
[tex]\[
5a + a + 5c = b
\][/tex]
Simplify this to:
[tex]\[
6a + 5c = b
\][/tex]
4. Isolate [tex]\(a\)[/tex]:
Solve for [tex]\(a\)[/tex] by isolating it on one side of the equation. Subtract [tex]\(5c\)[/tex] from both sides:
[tex]\[
6a = b - 5c
\][/tex]
5. Divide by 6:
Finally, divide both sides by 6 to solve for [tex]\(a\)[/tex]:
[tex]\[
a = \frac{b - 5c}{6}
\][/tex]
Thus, the solution to the equation [tex]\(a + c = \frac{b - a}{5}\)[/tex] solved for [tex]\(a\)[/tex] is:
[tex]\[
a = \frac{b}{6} - \frac{5c}{6}
\][/tex]
