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

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.

Answer 2

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 = -(2)/(8)=-(1)/(4)`