To solve the equation [tex]\( 5x + 3y = 15 \)[/tex] for [tex]\( x \)[/tex], follow these steps:
1. Start with the given equation:
[tex]\[
5x + 3y = 15
\][/tex]
2. To isolate [tex]\( x \)[/tex], we need to get [tex]\( x \)[/tex] alone on one side of the equation. First, subtract [tex]\( 3y \)[/tex] from both sides of the equation:
[tex]\[
5x = 15 - 3y
\][/tex]
3. Now, to solve for [tex]\( x \)[/tex], divide both sides of the equation by 5:
[tex]\[
x = \frac{15 - 3y}{5}
\][/tex]
4. Simplify the right-hand side of the equation by splitting the fraction:
[tex]\[
x = \frac{15}{5} - \frac{3y}{5}
\][/tex]
5. Simplify the fractions:
[tex]\[
x = 3 - \frac{3y}{5}
\][/tex]
Hence, the solution for [tex]\( x \)[/tex] in terms of [tex]\( y \)[/tex] is:
[tex]\[
x = 3 - \frac{3y}{5}
\][/tex]
Among the given options, the correct one is:
[tex]\[ x = 3 - \frac{3}{5} y \][/tex]
