Solve for x: −4(3x+10)−2=54.

Answer 1

To solve the equation \(-4(3x + 10) - 2 = 54\), we can start by simplifying the left side of the equation.

1. Distribute the \(-4\) to both terms inside the parentheses:

\[ -4 \cdot 3x - 4 \cdot 10 - 2 = -12x - 40 - 2 \]

2. Combine the constants \(-40\) and \(-2\):

\[ -12x - 42 = 54 \]

3. Next, add \(42\) to both sides of the equation to isolate the term with \(x\):

\[ -12x - 42 + 42 = 54 + 42 \]

This simplifies to:

\[ -12x = 96 \]

4. Now, divide both sides by \(-12\) to solve for \(x\):

\[ x = \frac{96}{-12} = -8 \]

Thus, the solution is:

\[ x = -8 \]