To solve the equation
[tex]\[
\frac{3(6z + 8)}{6} = -3z + 10
\][/tex]
Step 1: Simplify the left-hand side of the equation.
[tex]\[
\frac{3(6z + 8)}{6}
\][/tex]
To simplify, we can distribute the 3 in the numerator first:
[tex]\[
\frac{18z + 24}{6}
\][/tex]
Next, divide each term inside the fraction by 6:
[tex]\[
\frac{18z}{6} + \frac{24}{6} = 3z + 4
\][/tex]
So the equation now is:
[tex]\[
3z + 4 = -3z + 10
\][/tex]
Step 2: Combine like terms by adding [tex]\(3z\)[/tex] to both sides of the equation.
[tex]\[
3z + 4 + 3z = -3z + 10 + 3z
\][/tex]
This simplifies to:
[tex]\[
6z + 4 = 10
\][/tex]
Step 3: Isolate [tex]\(z\)[/tex] by subtracting 4 from both sides of the equation.
[tex]\[
6z + 4 - 4 = 10 - 4
\][/tex]
This simplifies to:
[tex]\[
6z = 6
\][/tex]
Step 4: Solve for [tex]\(z\)[/tex] by dividing both sides of the equation by 6.
[tex]\[
z = \frac{6}{6}
\][/tex]
[tex]\[
z = 1
\][/tex]
Therefore, the value of [tex]\(z\)[/tex] is
[tex]\[
z = 1
\][/tex]
