Alright, let's solve the equation [tex]\(3(z + 2) = 9\)[/tex] step by step.
1. Distribute the 3 on the left-hand side:
[tex]\[
3(z + 2) = 3 \cdot z + 3 \cdot 2 = 3z + 6
\][/tex]
So, the equation becomes:
[tex]\[
3z + 6 = 9
\][/tex]
2. Isolate the term containing the variable [tex]\(z\)[/tex]:
To do this, subtract 6 from both sides of the equation:
[tex]\[
3z + 6 - 6 = 9 - 6
\][/tex]
Simplifying both sides, we get:
[tex]\[
3z = 3
\][/tex]
3. Solve for [tex]\(z\)[/tex]:
Now, divide both sides of the equation by 3 to isolate [tex]\(z\)[/tex]:
[tex]\[
\frac{3z}{3} = \frac{3}{3}
\][/tex]
Simplifying this, we obtain:
[tex]\[
z = 1
\][/tex]
Therefore, the solution to the equation [tex]\(3(z + 2) = 9\)[/tex] is [tex]\(z = 1\)[/tex].
