Solve Multi-Step Linear Equations Quick Check

Question

5 of 55 of 5 Items

Question
Solve for x : 20x−5(6x+15)=−45 .(1 point)
Responses

x=2
x equals 2

x=−3
x equals negative 3

x=−2
x equals negative 2

x=3
x equals 3

Answer 1

To solve the equation \( 20x - 5(6x + 15) = -45 \), let's follow the steps:

1. Distribute the \(-5\) across the terms in the parentheses: \[ 20x - 5 \cdot 6x - 5 \cdot 15 = -45 \] Which simplifies to: \[ 20x - 30x - 75 = -45 \]

2. Combine like terms: \[ (20x - 30x) - 75 = -45 \] This simplifies to: \[ -10x - 75 = -45 \]

3. Add \(75\) to both sides of the equation to isolate the term with \(x\): \[ -10x = -45 + 75 \] Simplifying the right side: \[ -10x = 30 \]

4. Divide both sides by \(-10\): \[ x = \frac{30}{-10} = -3 \]

The solution for \(x\) is: \[ \boxed{-3} \]

Thus, the correct response is \(x = -3\).