Question

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

Answer 1

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