Justify each step in the proof below (You may use a choice more than once. You will not use all the choices given. )

Question

EG = 68

Given : EG = 68

Prove: x = 8

1. EG = 68, EF = 8x-12, FG = 2x 

2. EF + FG = EG 2. Response area

3. 8x - 12 + 2x = 68 3.

3. Response area

4. 10x - 12 = 68                                            4. Response area

5. 10x = 80                                                       5. 
Response area

6. x = 8                                                             6. 

Answer 1

1. Given: EG = 68 and the lengths EF and FG are expressed in terms of x as EF = 8x - 12 and FG = 2x.

2. The sum of the lengths EF and FG should be equal to the length EG according to the triangle equality theorem.

3. Substitute the expressions for EF and FG into the equation from step 2: 8x - 12 + 2x = 68.

4. Combine like terms on the left side of the equation: 10x - 12 = 68.

5. Add 12 to both sides of the equation: 10x - 12 + 12 = 68 + 12.

6. Simplify: 10x = 80.

7. Divide both sides of the equation by 10 to solve for x: (10x)/10 = 80/10.

8. Simplify: x = 8.