Question

F is between E and G on line EG. Ef=4x-8, FG=3x-16, and Eg=60. Find x, EF, and FG.

a) x = 12, EF = 44, FG = 32
b) x = 14, EF = 56, FG = 42
c) x = 10, EF = 32, FG = 26
d) x = 16, EF = 68, FG = 50

Answer 1

To find x, EF, and FG, set up equations using the given information. Solve the equations to find x = 12, EF = 44, FG = 32. Choose option a) as the correct answer.

Step-by-step explanation:

To find the values of x, EF, and FG, we can set up equations using the given information:

EF = 4x - 8,

FG = 3x - 16,

Eg = 60.

Since F is between E and G on line EG, we can set up the following equation:

EF + FG = Eg.

Substituting the equations for EF and FG, we have:

(4x - 8) + (3x - 16) = 60.

Combining like terms, we get:

7x - 24 = 60.

Adding 24 to both sides, we have:

7x = 84.

Dividing both sides by 7, we get:

x = 12.

Substituting x = 12 into the equations for EF and FG, we can find the values:

EF = 4(12) - 8 = 44,

FG = 3(12) - 16 = 32.

Therefore, the correct answer is option a) x = 12, EF = 44, FG = 32.