Question

1. when e is the midpoint of \\(\overline{ag}\\), find ae.

a ----e ----g
3x + 3 5x - 11
x=
ae=
my answer
ae=
a 7
b 24
c 35
d 48

Explanation:

Step1: Set AE equal to EG (midpoint property)

Since \( E \) is the midpoint of \( \overline{AG} \), \( AE = EG \). So we set the expressions equal: \( 3x + 3 = 5x - 11 \).

Step2: Solve for \( x \)

Subtract \( 3x \) from both sides: \( 3 = 2x - 11 \).
Add 11 to both sides: \( 14 = 2x \).
Divide by 2: \( x = 7 \).

Step3: Find \( AE \)

Substitute \( x = 7 \) into \( AE = 3x + 3 \):
\( AE = 3(7) + 3 = 21 + 3 = 24 \).

Answer:

\( x = 7 \), \( AE = 24 \) (and the option is B. 24)