To solve the equation [tex]\(2x + 3y = 5\)[/tex] for [tex]\(x\)[/tex], follow these steps:
1. Isolate the term involving [tex]\(x\)[/tex]:
Start with the given equation.
[tex]\[
2x + 3y = 5
\][/tex]
Subtract [tex]\(3y\)[/tex] from both sides to isolate the [tex]\(2x\)[/tex] term.
[tex]\[
2x = 5 - 3y
\][/tex]
2. Solve for [tex]\(x\)[/tex]:
Divide both sides of the equation by 2 to solve for [tex]\(x\)[/tex].
[tex]\[
x = \frac{5 - 3y}{2}
\][/tex]
3. Simplify the expression:
The expression [tex]\(\frac{5 - 3y}{2}\)[/tex] cannot be simplified further in a way that results in a simpler or more conventional form.
So, the correct form of [tex]\(x\)[/tex] when isolating it in the equation [tex]\(2x + 3y = 5\)[/tex] is:
[tex]\[
x = \frac{5 - 3y}{2}
\][/tex]
Now, comparing this with the provided choices:
1. [tex]\(x = -3y + \frac{5}{2}\)[/tex]
2. [tex]\(x = \frac{-3}{2} y + 5\)[/tex]
3. [tex]\(x = \frac{-3y + 5}{2}\)[/tex]
4. [tex]\(x = \frac{3y + 5}{2}\)[/tex]
The expression we derived, [tex]\(x = \frac{5 - 3y}{2}\)[/tex], matches the third option if you rearrange the numerator.
Therefore, the correct choice is:
[tex]\[
\boxed{\frac{-3y + 5}{2}}
\][/tex]
This corresponds to the third option:
[tex]\[
x = \frac{-3y + 5}{2}
\][/tex]
