Solve the following equation for [tex]\( x \)[/tex]:

[tex]\[ 2x + 5y = 8 \][/tex]

A. [tex]\( x = \frac{5}{2} y + 4 \)[/tex]

B. [tex]\( x = -\frac{5}{2} y - 4 \)[/tex]

C. [tex]\( x = \frac{5}{2} y - 4 \)[/tex]

D. [tex]\( x = -\frac{5}{2} y + 4 \)[/tex]



Answer :

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]