Question

o is the mid - point of segment fg. draw a picture, write an equ of each segment.

1. fo = 3x + 17, og = 7x - 15
2. fo = x

x =
fo =
og =
fg =

Explanation:

Step1: Use mid - point property

Since O is the mid - point of segment FG, then FO = OG. So we set up the equation $3x + 17=7x - 15$.

Step2: Isolate x terms on one side

Subtract $3x$ from both sides: $3x+17-3x=7x - 15-3x$, which simplifies to $17 = 4x-15$.

Step3: Isolate the term with x

Add 15 to both sides: $17 + 15=4x-15 + 15$, getting $32 = 4x$.

Step4: Solve for x

Divide both sides by 4: $\frac{32}{4}=\frac{4x}{4}$, so $x = 8$.

Step5: Find FO

Substitute $x = 8$ into the expression for FO: $FO=3x + 17=3\times8+17=24 + 17=41$.

Step6: Find OG

Substitute $x = 8$ into the expression for OG: $OG=7x - 15=7\times8-15=56 - 15=41$.

Step7: Find FG

Since FG=FO + OG and FO = OG = 41, then FG=41+41 = 82.

Answer:

$x = 8$, $FO = 41$, $OG = 41$, $FG = 82$