How many solutions does each equation have?

Equation No solution One solution Many solutions

1. 2x-2=2x+32x-2=2x+3

2. 5m-4=7m+85m-4=7m+8

3. y+7=y-3

1.

2x-2=2x+32x-2=2x+3

notice

2x-3=2x+2

minus 2x both sides

-3=2

false

no solution

2. 5m-4=7m+85m-4

add 4 to both sides

5m=92m

therefor m=0

but wait

5m-4=7m+8

5 (0) - 4=7 (0) + 8

-4=8

false

no solution

3.

y+7=y-3

minus y both sides

7=-3

false

no solution

none of them have solutions