Question

Jonathan found that the correct equation -2|8-x|-6=-12 had two possible solutions: x=5 and x=-11. Which explains whether his solutions are correct?

A) He is correct because both solutions satisfy the equation.

B) He is not correct because he made a sign error.

C) He is not correct because there are no solutions.

D) He is not correct because there is only one solution: x=5​

Answer 1

Explanation:

if you want to find the solutions here is a method:

-2|8-x|-6=-12

divid by -2 :

|8-x|+3=6

|8-x| = 3

8-x = 3 or 8-x=-3

x= 5 or x=11

Answer 2

D

Explanation:

Check the solutions by substituting the values of x into the left side of the equation and if equal to the right side then they are a solution.

x = 5

- 2 | 8 - 5 | - 6 = - 2 | 3 | - 6 = (- 2 × 3) - 6 = - 6 - 6 = - 12 ← correct

x = - 11

- 2 | 8 + 11 | - 6 = - 2 | 19 | - 6 = (- 2 × 19) - 6 = - 38 - 6 = - 44 ≠ - 12

Thus x = 5 is a solution but x = - 11 is not → D

The solutions to the equation are in fact x = 5 and x = 11