Since MN is the midsegment, then the proportion of the side is equal to 1/2. Thus the equation for finding x is the following equation.
[tex]\frac{2x+3}{9x-44}=\frac{1}{2}[/tex]
Thus, to solve for the value of x, multiply both sides of the equation by 2(9x-44). This will eliminate the denominators.
[tex]2(2x+3)=9x-44[/tex]
Simplify both sides of the equation.
[tex]4x+6=9x-44[/tex]
Isolate the variables on one side of the equation by subtracting 4x and adding 44 to both sides of the equation.
[tex]\begin{gathered} 6+44=9x-4x \\ 50=5x \end{gathered}[/tex]
To obtain the value of x, divide both sides of the equation by 5.
[tex]\begin{gathered} \frac{50}{5}=\frac{5x}{5} \\ 10=x \end{gathered}[/tex]
Thus, the value of x is 10.
To solve for MN, substitute the value of x, which is 10, into the expression 2x+3 and then simplify.
[tex]\begin{gathered} MN=2(10)+3 \\ MN=20+3 \\ MN=23 \end{gathered}[/tex]
To solve for AB, substitute the value of x, which is 10, into the expression 9x-44 and then simplify.
[tex]\begin{gathered} AB=9(10)-44 \\ AB=90-44 \\ AB=46 \end{gathered}[/tex]
Notice that AB is twice the measure of MN.
Therefore the answers in the blanks should be:
Equation: 2(2x+3)=9x-44
[tex]\begin{gathered} x=10 \\ MN=23 \\ AB=46 \end{gathered}[/tex]
