To check for equivalence, use properties of operations such as the Distributive Property. Two expression are said to be equivalent if they resulted in the same number after evaluation of each. You can both expand and factor expressions to generate equivalent expressions.
a) x+5 = 7
b) 2x - 8 = 20
c) 4x - 6x = 200
d) x+1= 5
3
a) x + 5 = 7
x + 5 - 5 = 7 - 5 (Subtract 5 from both sides)
x = 2
b) 2x - 8 = 20
2x - 8 + 8 = 20 + 8 (Add 8 to each side)
2x = 28
2x/2 = 28/2 (Divide each side by 2)
x = 14
c) 4x - 6x = 200
-2x = 200
-2x/-2 = 200/-2 (Divide each side by -2)
x = -100 (Note that a negative number divided by a negative number is positive, whereas a positive number divided by a negative number is negative)
d) x + 1 = 5
x + 1 - 1 = 5 - 1 (Subtract 1 from each side)
x = 4