To solve the equation [tex]\(8x + 3y = 6\)[/tex] for [tex]\(y\)[/tex], we will isolate [tex]\(y\)[/tex] on one side of the equation. Here are the steps:
1. Start with the given equation:
[tex]\[
8x + 3y = 6
\][/tex]
2. Subtract [tex]\(8x\)[/tex] from both sides to begin isolating [tex]\(y\)[/tex]:
[tex]\[
3y = 6 - 8x
\][/tex]
3. Divide every term by 3 to solve for [tex]\(y\)[/tex]:
[tex]\[
y = \frac{6 - 8x}{3}
\][/tex]
4. Simplify the right-hand side:
[tex]\[
y = \frac{6}{3} - \frac{8x}{3}
\][/tex]
5. Perform the division in each term:
[tex]\[
y = 2 - \frac{8x}{3}
\][/tex]
So, the solution for [tex]\(y\)[/tex] in terms of [tex]\(x\)[/tex] is:
[tex]\[
y = 2 - \frac{8x}{3}
\][/tex]
