To solve the equation [tex]\( 5x + 10y = 15 \)[/tex] for [tex]\( x \)[/tex], follow these steps:
1. Start with the given equation:
[tex]\[
5x + 10y = 15
\][/tex]
2. Isolate the term involving [tex]\( x \)[/tex]:
Subtract [tex]\( 10y \)[/tex] from both sides:
[tex]\[
5x = 15 - 10y
\][/tex]
3. Solve for [tex]\( x \)[/tex]:
Divide both sides of the equation by 5:
[tex]\[
x = \frac{15 - 10y}{5}
\][/tex]
4. Simplify the expression:
Break the fraction into two terms:
[tex]\[
x = \frac{15}{5} - \frac{10y}{5}
\][/tex]
5. Reduce the terms:
Simplify each fraction:
[tex]\[
x = 3 - 2y
\][/tex]
6. State the final result:
[tex]\[
x = 3 - 2y
\][/tex]
Therefore, the correct answer is:
[tex]\[
\boxed{A. \, x = -2y + 3}
\][/tex]
Note that [tex]\( x = -2y + 3 \)[/tex] is equivalent to [tex]\( x = 3 - 2y \)[/tex].
