Question

1. if f is the mid - point of $overline{eg}$, $eg = 22$, and $ef = 4x - 3$, then which of the following is the value of x? (1) $3\frac{1}{2}$ (2) $4\frac{3}{4}$ (3) $6\frac{1}{4}$ (4) $8\frac{1}{3}$

Explanation:

Step1: Use mid - point property

Since \(F\) is the mid - point of \(\overline{EG}\), then \(EF=\frac{1}{2}EG\).

Step2: Substitute given values

We know that \(EG = 22\) and \(EF=4x - 3\). So, \(4x-3=\frac{22}{2}\).

Step3: Simplify the right - hand side

\(\frac{22}{2}=11\), so the equation becomes \(4x - 3=11\).

Step4: Solve for \(x\)

Add 3 to both sides of the equation: \(4x=11 + 3\), so \(4x=14\). Then divide both sides by 4: \(x=\frac{14}{4}=\frac{7}{2}=3\frac{1}{2}\).

Answer:

(1) \(3\frac{1}{2}\)