Question

If DE = 13x − 20, EF = 7x, and DF = 18x + 6, what is DF?

Answer 1

In this problem, we are going to apply the segement addition property. It simply states the following with respect to your problem:

$\overline{DE}+\overline{EF}=\overline{DF}$

From the diagram, we are given the following information:

$\begin{gathered} DE=13x-20 \\ \\ EF=7x \\ \\ DF=18x+6 \end{gathered}$

Using the segment addition property, we can substitute the expressions for DE, EF, and DF to create and solve an equation:

$(13x-20)+(7x)=18x+6$

Combine like terms of the left-hand side:

$\begin{gathered} 13x+7x-20=18x+6 \\ \\ 20x-20=18x+6 \end{gathered}$

Add 20 to both sides of the equation:

$\begin{gathered} 20x-20+20=18x+6+20 \\ \\ 20x=18x+26 \end{gathered}$

Subtract 8x from both sides:

$\begin{gathered} 20x-18x=18x-18x+26 \\ \\ 2x=26 \end{gathered}$

Divide both sides by 2:

$\begin{gathered} \frac{2x}{2}=\frac{26}{2} \\ \\ x=13 \end{gathered}$

Now we know the value of x is 13. We will use that to find DF:

$DF=18x+6=18(13)+6=240$

The length of DF is 240 units.