Solve the following linear equation.

Question

-8(2x+17)=19
x=

(Note: if the answer is an infinite repeating decimal your answer must be in fraction form. So 0.333... = 1/3)

Answer 1

To solve the equation \(-8(2x + 17) = 19\), we will start by distributing \(-8\) on the left side of the equation.

1. Distribute \(-8\): \[ -8 \cdot 2x - 8 \cdot 17 = 19 \] This simplifies to: \[ -16x - 136 = 19 \]

2. Next, we isolate the term with \(x\) by adding \(136\) to both sides: \[ -16x = 19 + 136 \] Which simplifies to: \[ -16x = 155 \]

3. Now, divide both sides by \(-16\) to solve for \(x\): \[ x = \frac{155}{-16} \] This can also be written as: \[ x = -\frac{155}{16} \]

Thus, the solution to the equation is: \[ \boxed{-\frac{155}{16}} \]