2. For each of the following statements, indicate whether it is "Always True", "Never True", or "Sometimes True". Mark an "X" in the appropriate column. If you choose "Sometimes True"
then state when it is true. The first one is done as an example.
Always True
Never True
Sometimes
True
It is true when...
x-12=x+30

1. Never True               2. Always True             3. Never True

4. Sometimes True (True when x = 0)             5. Never True

Step-by-step explanation:

1. x - 12 = x + 30

subtract x from both sides

-12 = 30

add 12 to both sides

0 = 42

Never True (no solutions)

2. 2(x+6) = 2x + 12

2x + 12 = 2x + 12

Always True (infinite solutions)

3. 3(x - 2) = 3x - 2

3x - 6 = 3x - 2

subtract 3x from both sides

-6 = -2

Never True (no solutions)

4. (x + 4)^2 = x^2 + 4^2

(x+4)^2 = (x+4)(x+4)

x^2 + 8x + 16 = x^2 + 4^2

subtract x^2 from both sides

8x + 16 = 16

subtract 16 from both sides

8x = 0

divide both sides by 8

x = 0

Sometimes True. It is true when x = 0.

5. x^2 + 4 = 0

Move 4 to the right

x^2 = -4

This statement is false because any value multiplied by itself (squared) can not equal a negative number.

Never True (no solutions)

Hope this helps!