F is the midpoint of EG. If EF = x + 3 and EG = 3x + 1, what is EF? E x + 3 F 3x + 1 G Simplify your answer and write it as a proper fraction, mixed number, or integer.

Question

asked May 8, 2024 189k views

1 Answer

Mrugesh Mistry · Answer 1 · 2024-05-12T06:03:26+0000

Answer:

EF = 8

Explanation:

F is the midpoint of EG. So, the distance of EF and GF will be same and if we add EF and GF, it will give the total distance of EG.

GF = EF

GF = x + 3

EG = GF + EF

Substitute the value of EG, GF and Ef in the above equation.

3x + 1 = x + 3 + x + 3

Combine the like terms in the RHS,

3x + 1 = 2x + 6

Subtract 1 from both sides,

3x = 2x + 6 - 1

3x = 2x + 5

Subtract 2x from both sides,

3x - 2x = 5

$\boxed{\bf x = 5}$

Now, we can find EF.

EF = x + 3

= 5 + 3

= 8

Answer: EF = 8