Answer
a) All reals
b) No solution
c) 0
d) 0
e) No solution
f) All reals
g) No solutions
h) All reals
i) 0
Work Step by Step
We simplify each side of the expression. If the two sides of the equation are the same, the solution is all real numbers. If they are two values that cannot be equal, the answer is no solution.
a) $ -2x + 2 = -2x +2 \space \text{all real numbers}$
b) $3x + 4 = 3x -4 \\ 4 = -4 \space \text{no solution}$
c) $ 5x - 5 = -5x -5 \\ 10x =0 \\ x=0$
d) $\frac{x-3}{3} = -1 \\ x-3 = -3 \\ x = 0$
e) $1 = \frac{-2-2}{3} \\ 1 = -4/3 \space \text{no solution}$
f) $ -2 = -10/5 \\ -2 = -2 \space \text{all real numbers}$
g) $4x-8 -2x -6 = 2x +6 \\ -14 =6 \space \text{no solution}$
h) $ 5x+15 -3x +15 = 2x + 30 \\ 30 = 30 \space \text{all real numbers}$
i) $ 7x -7 +4x-8 = 15x -15 \\ 4x =0 \\ x =0 $
