To solve the equation [tex]\(2x + 5y = 8\)[/tex] for [tex]\(x\)[/tex] and then identify which solution from the given choices is correct, follow these steps:
1. Start with the given equation:
[tex]\[
2x + 5y = 8
\][/tex]
2. Isolate [tex]\(x\)[/tex] by moving the term involving [tex]\(y\)[/tex] to the other side:
[tex]\[
2x = 8 - 5y
\][/tex]
3. Solve for [tex]\(x\)[/tex] by dividing both sides of the equation by 2:
[tex]\[
x = \frac{8 - 5y}{2}
\][/tex]
Which simplifies to:
[tex]\[
x = 4 - \frac{5}{2}y
\][/tex]
4. Write the simplified form of [tex]\(x\)[/tex]:
[tex]\[
x = -\frac{5}{2}y + 4
\][/tex]
Now, let's match our solution to the given choices:
- [tex]\(x = \frac{5}{2} y + 4\)[/tex]
- [tex]\(x = -\frac{5}{2} y - 4\)[/tex]
- [tex]\(x = \frac{5}{2} y - 4\)[/tex]
- [tex]\(x = -\frac{5}{2} y + 4\)[/tex]
The solution we obtained is:
[tex]\[
x = -\frac{5}{2} y + 4
\][/tex]
Therefore, the correct choice that matches our solution is:
[tex]\[
x = -\frac{5}{2} y + 4
\][/tex]
Among the provided choices, this is the fourth one. Hence, the correct answer is:
[tex]\[
\boxed{4}
\][/tex]
