Question

The equation below was solved incorrectly. Study the work below.
5x + 5 = -3(x - 1)

Step 1: 5x + 5= -3x + 3

Step 2: 2x= -2

Step 3: x = -1

1. Describe the mistake in the work shown above.

2. What is the solution to the equation 5x + 5= -3(x - 1) ? Show all work

Answer 1

Start with

$5x+5=-3(x-1)$

Distribute the -3 on the right hand side:

$5x+5=-3x+3$

Add 3x-5 to both sides:

$8x=-2 \leftarrow \text{here's the mistake!}$

Divide both sides by 8:

$x = -\dfrac{2}{8}=-\dfrac{1}{4}$

Answer 2

Answer:

Step-by-step explanation:

Step 1 is correct: 5x + 5 = -3x + 3

add 3x to both sides: 8x + 5 = 3

add -5 to both sides: 8x = -2

divide both sides by 8: x=-1/4

check answer by inserting -1/4 for x into original equation:

5(-1/4) + 5 = -3(-1/4-1)

-5/4 + 20/4 = 3/4 + 3

15/4 = 3/4 + 12/4

15/4 = 15/4 so answer of -1/4 is correct.