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

[tex]\[ 5x + 3y = 15 \][/tex]

A. [tex]\( x = -\frac{3}{5} y - 3 \)[/tex]
B. [tex]\( x = -\frac{3}{5} y + 3 \)[/tex]
C. [tex]\( x = \frac{3}{5} y + 3 \)[/tex]
D. [tex]\( x = \frac{3}{5} y - 3 \)[/tex]

Sagot :

GinnyAnswer
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]
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