To solve the given equation [tex]\( 5x + 10y = 15 \)[/tex] for [tex]\( x \)[/tex], we need to isolate [tex]\( x \)[/tex] on one side of the equation. Let's go through the steps to do this carefully:
1. Start with the given equation:
[tex]\[
5x + 10y = 15
\][/tex]
2. Subtract [tex]\( 10y \)[/tex] from both sides to begin isolating [tex]\( x \)[/tex]:
[tex]\[
5x = 15 - 10y
\][/tex]
3. Divide every term in the equation by 5 to solve for [tex]\( x \)[/tex]:
[tex]\[
x = \frac{15 - 10y}{5}
\][/tex]
4. Simplify the right side of the equation:
[tex]\[
x = \frac{15}{5} - \frac{10y}{5}
\][/tex]
This simplifies further to:
[tex]\[
x = 3 - 2y
\][/tex]
5. Rewriting it to match the given options:
[tex]\[
x = -2y + 3
\][/tex]
Thus, the solution is:
[tex]\[
\boxed{B: x = -2y + 3}
\][/tex]
