To solve the equation [tex]\(8x - y = 5\)[/tex] for [tex]\(y\)[/tex], follow these steps:
1. Start with the given equation:
[tex]\[ 8x - y = 5 \][/tex]
2. To isolate [tex]\(y\)[/tex], we need to move all other terms to the opposite side of the equation. Begin by subtracting [tex]\(8x\)[/tex] from both sides of the equation:
[tex]\[ -y = 5 - 8x \][/tex]
3. Now, we need to get [tex]\(y\)[/tex] by itself. Since [tex]\(y\)[/tex] currently has a negative sign (i.e., [tex]\(-y\)[/tex]), multiply both sides of the equation by [tex]\(-1\)[/tex]:
[tex]\[ y = -1 \cdot (5 - 8x) \][/tex]
4. Distribute the [tex]\(-1\)[/tex] through the parentheses:
[tex]\[ y = -5 + 8x \][/tex]
5. Finally, rearrange the terms to present [tex]\(y\)[/tex] in a standard form:
[tex]\[ y = 8x - 5 \][/tex]
Thus, the solution to the equation [tex]\(8x - y = 5\)[/tex] for [tex]\(y\)[/tex] is:
[tex]\[ \boxed{y = 8x - 5} \][/tex]
