Solve Multi-Step Linear Equations Quick Check

Question

4 of 54 of 5 Items

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

x=8
x equals 8

x=4
x equals 4

x=−8
x equal negative 8

x=−4

Answer 1

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

1. Distribute \(-4\) to both 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 of the equation to isolate the term with \(x\): \[ -12x = 54 + 42 \] \[ -12x = 96 \]

4. Now, divide both sides by \(-12\): \[ x = \frac{96}{-12} \] \[ x = -8 \]

So the solution is: \[ x = -8 \]

The correct response is \(x = -8\) (or "x equals negative 8").