Questions: Point F is on line segment EG. Given FG=8, EF=2x+4, and EG=4x-10, determine the numerical length of EF.

Solution Steps

To determine the numerical length of $\overline{E F}$, we can use the fact that the sum of the lengths of the segments $\overline{E F}$ and $\overline{F G}$ is equal to the length of the segment $\overline{E G}$. This gives us the equation $E F + F G = E G$. We can then solve for $x$ and use it to find the length of $\overline{E F}$.

Given:

• \( F G = 8 \)
• \( E F = 2x + 4 \)
• \( E G = 4x - 10 \)

We know that \( E F + F G = E G \). Therefore, we can set up the equation: \[ 2x + 4 + 8 = 4x - 10 \]

Simplify the equation: \[ 2x + 12 = 4x - 10 \]

Rearrange the equation to solve for \( x \): \[ 2x + 12 = 4x - 10 \] \[ 12 + 10 = 4x - 2x \] \[ 22 = 2x \] \[ x = 11 \]

Substitute \( x = 11 \) back into the expression for \( E F \): \[ E F = 2x + 4 \] \[ E F = 2(11) + 4 \] \[ E F = 22 + 4 \] \[ E F = 26 \]

Final Answer