To solve the equation [tex]\(\frac{1}{4} x + 25 y = -1\)[/tex] for [tex]\(x\)[/tex] in terms of [tex]\(y\)[/tex], we need to isolate [tex]\(x\)[/tex]. Here are the detailed steps:
1. Starting Equation:
[tex]\[
\frac{1}{4} x + 25 y = -1
\][/tex]
2. Move the term involving [tex]\(y\)[/tex] to the right-hand side:
To isolate [tex]\(x\)[/tex], we subtract [tex]\(25y\)[/tex] from both sides of the equation:
[tex]\[
\frac{1}{4} x = -1 - 25 y
\][/tex]
3. Eliminate the fraction:
To get rid of the fraction, multiply both sides of the equation by 4:
[tex]\[
x = 4(-1 - 25 y)
\][/tex]
4. Simplify the right-hand side:
Distribute the 4 on the right-hand side:
[tex]\[
x = 4(-1) + 4(-25 y)
\][/tex]
[tex]\[
x = -4 - 100 y
\][/tex]
The solution for [tex]\(x\)[/tex] in terms of [tex]\(y\)[/tex] is:
[tex]\[
x = -4 - 100 y
\][/tex]
