Question

Solve Multi-Step Linear Equations Quick Check
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 \(x = -3\).