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: $$\boxed{{\displaystyle -3}}$$

Thus, the correct response is $x=-3$.