Justify each step in the proof below (You may use a choice more than once. You will not use all the choices given. )
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.
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.
Step 1: Given that EG = 68 and we have EF = 8x-12 and FG = 2x.
Step 2: We can use the fact that the sum of the two sides of a triangle equals the third side. So EF + FG = EG.
Step 3: Substitute the values of EF and FG into the equation from step 2. 8x-12 + 2x = 68.
Step 4: Simplify the equation from step 3. Combine like terms on the left side, we get 10x - 12 = 68.
Step 5: Add 12 to both sides of the equation from step 4 to isolate the variable. We get 10x = 80.
Step 6: Divide both sides of the equation from step 5 by 10 to solve for x. We get x = 8.
Step 7: Proved that x = 8 based on the given information and logical deductions.
Step 1: The given information states that EG is equal to 68.
Step 2: We know that the sum of EF and FG is equal to EG. This can be written as EF + FG = EG.
Step 3: Substituting the expressions given in step 1, we have 8x - 12 + 2x = 68.
Step 4: Combining like terms, we simplify the equation to obtain 10x - 12 = 68.
Step 5: To isolate the variable, we add 12 to both sides of the equation. This yields 10x = 80.
Step 6: Finally, we divide both sides of the equation by 10, giving us x = 8 as the solution.