Question

Error Analysis You and a friend are doing math homework together. You have to solve the equation 5x + 4x - 68 = 34 - 8x. Your friend arrives at the incorrect answer x = -2. Find the correct value of x. Then find the error your friend possibly made. X x=0 What possible error could your friend have made to get x = -2? OA. Your friend should have added 68 to each side of the equation, but instead subtracted 68 from the right side. OB. Your friend should have added 8x to each side of the equation, but instead subtracted 8x from the left side. OC. Your friend should have added 5x and 4x to get a sum of 9x, but instead got a sum of 8x. ​

Answer 1

This is probably what steps your friend took, or something similar.

5x+4x-68 = 34-8x

9x = 34-8x-68

9x = -8x-34

9x+8x = -34

17x = -34

x = -34/17

x = -2

However, the error is when they subtracted 68 from both sides (line 2).

Instead, they should have added 68 to each side to undo the -68 on the left hand side.

----------------------------

Here's what the steps should look like (one variation of it anyway)

5x+4x-68 = 34-8x

9x = 34-8x+68

9x = -8x+102

9x+8x = 102

17x = 102

x = 102/17

x = 6 is the correct value of x

--------------------------

Check:

5x+4x-68 = 34-8x

5*6+4*6-68 = 34-8*6

30+24-68 = 34-48

54-68 = 34-48

-14 = -14

We get the same thing on both sides after replacing each x with 6, so it confirms x = 6 is the solution.

If you were to try x = -2, then you would end up with -86 = 50 which is a false statement. So that rules out x = -2 as a solution.