To solve the equation [tex]\( 12 = 15\left(z - \frac{1}{5}\right) \)[/tex] for [tex]\( z \)[/tex], follow these steps:
1. Distribute the 15:
[tex]\[
12 = 15z - 15 \cdot \frac{1}{5}
\][/tex]
2. Simplify the term with the fraction:
[tex]\[
15 \cdot \frac{1}{5} = 3
\][/tex]
Thus, the equation becomes:
[tex]\[
12 = 15z - 3
\][/tex]
3. Isolate the term with [tex]\( z \)[/tex] by adding 3 to both sides of the equation:
[tex]\[
12 + 3 = 15z - 3 + 3
\][/tex]
Simplify:
[tex]\[
15 = 15z
\][/tex]
4. Solve for [tex]\( z \)[/tex] by dividing both sides of the equation by 15:
[tex]\[
\frac{15}{15} = \frac{15z}{15}
\][/tex]
Simplify:
[tex]\[
1 = z
\][/tex]
Hence, the solution for [tex]\( z \)[/tex] is:
[tex]\[
z = 1
\][/tex]
