To solve the equation [tex]\(2(x - 3) = 7\)[/tex], we can follow these steps:
1. Distribute the 2 on the left side:
We expand the left-hand side of the equation:
[tex]\[
2(x - 3) = 2x - 6
\][/tex]
2. Set the left side equal to the right side:
The equation now becomes:
[tex]\[
2x - 6 = 7
\][/tex]
3. Add 6 to both sides:
To isolate the term with [tex]\(x\)[/tex] on one side, we add 6 to both sides of the equation:
[tex]\[
2x - 6 + 6 = 7 + 6
\][/tex]
Simplifying, we get:
[tex]\[
2x = 13
\][/tex]
4. Divide both sides by 2:
To solve for [tex]\(x\)[/tex], we divide both sides of the equation by 2:
[tex]\[
\frac{2x}{2} = \frac{13}{2}
\][/tex]
Simplifying, we find:
[tex]\[
x = \frac{13}{2}
\][/tex]
So, the solution to the equation [tex]\(2(x - 3) = 7\)[/tex] is [tex]\(x = \frac{13}{2}\)[/tex], which corresponds to option (e).
