To solve the given equation [tex]\(\frac{1}{3}(2x + 3) = 3\)[/tex], follow these detailed steps:
1. Eliminate the Fraction:
- The first step is to eliminate the fraction by multiplying both sides of the equation by 3.
- This will simplify the equation and make it easier to solve.
[tex]\[
3 \cdot \frac{1}{3}(2x + 3) = 3 \cdot 3
\][/tex]
- Simplifying both sides:
[tex]\[
2x + 3 = 9
\][/tex]
2. Isolate the Variable [tex]\(x\)[/tex]:
- Next, we need to isolate the variable [tex]\(x\)[/tex] by getting rid of the constant term on the left side of the equation.
- We do this by subtracting 3 from both sides of the equation.
[tex]\[
2x + 3 - 3 = 9 - 3
\][/tex]
- Simplifying both sides:
[tex]\[
2x = 6
\][/tex]
3. Solve for [tex]\(x\)[/tex]:
- Now, we solve for [tex]\(x\)[/tex] by dividing both sides of the equation by 2.
[tex]\[
x = \frac{6}{2}
\][/tex]
- Simplifying the right side:
[tex]\[
x = 3
\][/tex]
Therefore, the solution to the equation [tex]\(\frac{1}{3}(2x + 3) = 3\)[/tex] is [tex]\(x = 3\)[/tex].
