Solve the following equation for xx. Express your answer in the simplest form. 3, left parenthesis, minus, 7, x, minus, 6, right parenthesis, equals, minus, 2, left parenthesis, x, minus, 6, right parenthesis 3(−7x−6)= −2(x−6)

Answer 1

To solve the equation \( 3(-7x - 6) = -2(x - 6) \), we will start by distributing both sides.

1. Distribute \( 3 \) on the left side: \[ 3(-7x) + 3(-6) = -21x - 18 \]

2. Distribute \( -2 \) on the right side: \[ -2(x) + 2(6) = -2x + 12 \]

Now, we can rewrite the equation: \[ -21x - 18 = -2x + 12 \]

Next, we will isolate \( x \). Start by adding \( 21x \) to both sides: \[ -18 = 21x - 2x + 12 \] This simplifies to: \[ -18 = 19x + 12 \]

Next, subtract \( 12 \) from both sides: \[ -18 - 12 = 19x \] This simplifies to: \[ -30 = 19x \]

Now, divide both sides by \( 19 \): \[ x = \frac{-30}{19} \]

Thus, the solution in simplest form is: \[ \boxed{\frac{-30}{19}} \]