Answer :
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]
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]
