Solve for x : −4(3x+10)−2=54 .(1 point) Responses x=−4 x equals negative 4 x=4 x equals 4 x=8 x equals 8 x=−8

Answer 1

To solve the equation \(-4(3x + 10) - 2 = 54\), follow these steps:

1. Distribute \(-4\) to the terms inside the parentheses: \[ -4 \cdot 3x - 4 \cdot 10 - 2 = 54 \] This simplifies to: \[ -12x - 40 - 2 = 54 \]

2. Combine the constants on the left side: \[ -12x - 42 = 54 \]

3. Add \(42\) to both sides to isolate the term with \(x\): \[ -12x = 54 + 42 \] Simplifying the right side gives: \[ -12x = 96 \]

4. Divide both sides by \(-12\) to solve for \(x\): \[ x = \frac{96}{-12} \] This simplifies to: \[ x = -8 \]

Thus, the solution is \(x = -8\).

The answer is: x = -8.