To solve the equation [tex]\(\frac{2}{3}(3x + 6) = 14\)[/tex], let's go through it step-by-step:
1. Eliminate the fraction:
Multiply both sides of the equation by 3 to get rid of the denominator:
[tex]\[
3 \cdot \frac{2}{3}(3x + 6) = 3 \cdot 14
\][/tex]
Simplifying this, we get:
[tex]\[
2(3x + 6) = 42
\][/tex]
2. Distribute the 2 on the left-hand side:
[tex]\[
2 \cdot 3x + 2 \cdot 6 = 42
\][/tex]
Simplifying further, we have:
[tex]\[
6x + 12 = 42
\][/tex]
3. Isolate the term with [tex]\(x\)[/tex]:
Subtract 12 from both sides of the equation to move the constant term to the right-hand side:
[tex]\[
6x + 12 - 12 = 42 - 12
\][/tex]
Simplifying this, we get:
[tex]\[
6x = 30
\][/tex]
4. Solve for [tex]\(x\)[/tex]:
Divide both sides of the equation by 6 to isolate [tex]\(x\)[/tex]:
[tex]\[
\frac{6x}{6} = \frac{30}{6}
\][/tex]
Simplifying this, we obtain:
[tex]\[
x = 5
\][/tex]
Therefore, the solution to the equation [tex]\(\frac{2}{3}(3x + 6) = 14\)[/tex] is [tex]\(x = 5\)[/tex].
