Mika used these steps to solve the equation 5x−12=−2+5(x−2)
. which choice describes the meaning of her result, −12=−12?

a. the result is not correct because the solution should be a positive integer

b. no values of x
make the equation true.

c. the solution is x = -12

d. all values of x make the equation true

5x−12=−2+5(x−2)
multiply 5 by all in parentheses first
5x - 12= -2 + (5*x) + (5*-2)
5x - 12= -2 + 5x - 10
5x - 12= 5x - 12
if you subtract 5x from one side and add 12 to the other the solution is:
0= 0

This equation is one that is always true. No matter what number you put in for x, it will always be true.

Example:
5x - 12= 5x - 12
5(4) - 12= 5(4) - 12
20 - 12= 20 - 12
8= 8

Example:
5(-100) - 12= 5(-100) - 12
-500 - 12= -500 - 12
-512= -512

This will happen no matter what number x is.

ANSWER: D) All values of x make the equation true.

Hope this helps! :)

D) all values of x make the equation true