help on some math problems. Major?

Question

1.How many values of x make 3x + 3 = 3(x + 1) a true statement?
2.How many values of x make 4x + 7 = 39 a true statement?

Answer 1

1) All values of x
2) One value of x (8)

In the first case you have:
3x + 3 = 3(x+1)

Distributing the 3 through on the right:
3x + 3 = 3x + 3

Subtracting 3 from both sides:
3x = 3x

Dividing by 3:
x = x

This is true for any value of x.

For the second case:
4x + 7 = 39

Subtract 7 from both sides:
4x = 32

Divide both sides by 4:
x = 8

This is only true for one value (x = 8).

Answer 2

1. All values of X since X = X
2. 1 value of X.
X = (39 - 7)/4 = 32/4 = 8

Answer 3

since 3(x+1) always equals 3x + 3, all values of x satisfy that equation, so there are an infinite number of values.

4x + 7 = 39
4x = 39 - 7 = 32
4x = 8, the only value to satisfy the equation.