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Let's begin by listing out the information given to us:
OF bisects |EOG|: we have |EOF| & |FOG|
|EOF| = 2x - 3; |FOG| = x + 10
Both |EOF| & |FOG| are equal because OF is the midpoint
To solve for the value of x, we equate |EOF| & |FOG|, we have:
[tex]\begin{gathered} |EOF|=|FOG|\Rightarrow2x-3=x+10 \\ 2x-x=10+3 \\ x=13 \end{gathered}[/tex]x = 13