To solve the equation [tex]\(-\frac{1}{y+5} = -6\)[/tex], let's go through it step by step.
1. Eliminate the negative signs by multiplying both sides of the equation by -1:
[tex]\[
\frac{1}{y+5} = 6
\][/tex]
2. Isolate the variable [tex]\( y \)[/tex] by cross-multiplying:
[tex]\[
1 = 6(y + 5)
\][/tex]
3. Distribute the 6 on the right-hand side:
[tex]\[
1 = 6y + 30
\][/tex]
4. Move the constant term on the right-hand side to the left-hand side by subtracting 30 from both sides:
[tex]\[
1 - 30 = 6y
\][/tex]
[tex]\[
-29 = 6y
\][/tex]
5. Solve for [tex]\( y \)[/tex] by dividing both sides of the equation by 6:
[tex]\[
y = \frac{-29}{6}
\][/tex]
So, the simplified answer is:
[tex]\[
y = -\frac{29}{6}
\][/tex]
