To solve the equation [tex]\(1 + 8x = -16 - 2x - 7x\)[/tex], follow these steps:
1. Simplify the terms on both sides of the equation. First, combine like terms on the right side:
[tex]\[
-16 - 2x - 7x = -16 - 9x
\][/tex]
So the equation now looks like:
[tex]\[
1 + 8x = -16 - 9x
\][/tex]
2. Move all terms involving [tex]\(x\)[/tex] to one side of the equation and the constant terms to the other side. To do this, add [tex]\(9x\)[/tex] to both sides of the equation and subtract 1 from both sides:
[tex]\[
1 + 8x + 9x = -16 - 9x + 9x - 1
\][/tex]
Simplifying this, we get:
[tex]\[
17x = -17
\][/tex]
3. Solve for [tex]\(x\)[/tex] by dividing both sides by 17:
[tex]\[
x = \frac{-17}{17}
\][/tex]
Simplifying this, we find:
[tex]\[
x = -1
\][/tex]
Thus, the solution to the equation [tex]\(1 + 8x = -16 - 2x - 7x\)[/tex] is [tex]\(x = -1\)[/tex].
### Answer:
B. [tex]\(x = -1\)[/tex]
