Question

1. 2x + 7 = 2x - 7

2. 3x + 8 = -2x + 8

3. 4(x + 1) = 4x + 4

Answer 1

1.
2x+7=2x-7
2x-2x=-7-7
0=-14
Math error.

2.
3x+8=-2x+8
3x+2x=8-8
5x=0
x=0


3.
4(x+1)=4x+4
4x+4=4x+4
4x-4x=4-4
0=0
Correct

Answer 2

Consider left and right sides of the equations as linear functions.

Then:

• 1. The equation 1 has lines with the same slope (2) but different y-intercepts (7 and -7), therefore the lines are parallel and no solution.
• 2. The lines have different slopes (3 and 2), therefore they intersect and there is one solution.
• 3. After opening the parenthesis we get both sides same, meaning the lines are same and overlap. The equation has infinitely many solutions.