Question

Solve for x to determine if the equation has one, none, or infinite solutions.
5(2x+2)−4=2x+6 (1 point)
Responses

The equation has infinite solutions.
The equation has infinite solutions.

The equation has one solution: x=1.
The equation has one solution: x equals 1 .

The equation has one solution: x=0.
The equation has one solution: x equals 0 .

The equation has no solution.

Answer 1

Solve the following linear equation for x . Then check your answer. Show all your steps for solving and checking.

5x+8+x=32

(4 points)

Answer 2

To solve for x:

5(2x+2)−4=2x+6
10x + 10 - 4 = 2x + 6
10x + 6 = 2x + 6
10x = 2x
8x = 0
x = 0

Therefore, the equation has one solution: x=0.

Answer 3

To solve the equation 5x + 8 + x = 32:

Combine like terms on the left side:
5x + 8 + x = 32
6x + 8 = 32

Subtract 8 from both sides:
6x + 8 - 8 = 32 - 8
6x = 24

Divide by 6 on both sides:
6x / 6 = 24 / 6
x = 4

Checking the answer:
5(4) + 8 + 4 = 32
20 + 8 + 4 = 32
32 = 32

Therefore, x = 4 is the correct solution.