To solve for [tex]\( z \)[/tex] in the equation [tex]\(\frac{8z + 4}{-4} = -9\)[/tex], follow these steps:
1. Clear the Denominator: Multiply both sides of the equation by [tex]\(-4\)[/tex] to eliminate the denominator.
[tex]\[
\frac{8z + 4}{-4} \cdot (-4) = -9 \cdot (-4)
\][/tex]
Simplifying this gives:
[tex]\[
8z + 4 = 36
\][/tex]
2. Isolate the Term with [tex]\( z \)[/tex]: Subtract 4 from both sides to isolate the [tex]\( 8z \)[/tex] term.
[tex]\[
8z + 4 - 4 = 36 - 4
\][/tex]
Simplifying this gives:
[tex]\[
8z = 32
\][/tex]
3. Solve for [tex]\( z \)[/tex]: Divide both sides by 8 to solve for [tex]\( z \)[/tex].
[tex]\[
\frac{8z}{8} = \frac{32}{8}
\][/tex]
Simplifying this gives:
[tex]\[
z = 4
\][/tex]
Thus, the solution to the equation [tex]\(\frac{8z + 4}{-4} = -9\)[/tex] is:
[tex]\[
z = 4
\][/tex]
