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 equal negative 8

x=8
x equals 8

x=−4
x equals negative 4

x=4

Answer 1

To solve the equation \(-4(3x + 10) - 2 = 54\), let's go through the steps:

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

2. Combine the constant terms: \[ -12x - 42 = 54 \]

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

4. Divide both sides by \(-12\): \[ x = \frac{96}{-12} \] Simplifying this gives: \[ x = -8 \]

Therefore, the solution is: \[ \boxed{-8} \]

So the correct response is \(x = -8\).