Question

Given collinear points E, F, and G such that point F is between E and G. Find the length of EG given that EG = 7x + 5, EF = 3x - 1, and FG = x + 33?

a) 23
b) 45
c) 52
d) 17

Answer 1

The length of EG is 68 units.

Step-by-step explanation:

We are given that EF = 3x - 1, FG = x + 33, and EG = 7x + 5.

Since F is between E and G on the same line, we can write the equation EF + FG = EG.

Substituting the given values, we have (3x - 1) + (x + 33) = 7x + 5.

Simplifying the equation, we get 4x + 32 = 7x + 5.

By subtracting 4x from both sides and subtracting 5 from both sides, we get 27 = 3x.

Dividing both sides by 3, we find x = 9.

Finally, we substitute the value of x back into the equation EG = 7x + 5 to find the length of EG: EG = 7(9) + 5 = 63 + 5 = 68.

Therefore, the length of EG is 68 units.