Question

Point Evis between D and F on D.if DE=4x+12,EF=7x-9, and DF=13x-11,then find x, DE ,&EF

Answer 1

Since E is a point between D and F, then, we can write an equation that follows:

`DE+EF=DF`

Replace with the corresponding expressions,

`(4x+12)+(7x-9)=(13x-11)`

group terms that are alike,

`11x+3=13x-11`

solve for x,

`\begin{gathered} 11x-13x=-11-3 \\ -2x=-14 \\ x=(-14)/(-2) \\ x=7 \end{gathered}`

then, replace x in the expressions DE and EF,

`\begin{gathered} DE=4x+12 \\ DE=4(7)+12 \\ DE=28+12 \\ DE=40 \\ \\ EF=7x-9 \\ EF=7(7)-9 \\ EF=49-9 \\ EF=40 \end{gathered}`

Answer:

`\begin{gathered} 1.\text{ }x=7 \\ 2.\text{ }DE=40 \\ 3.\text{ }EF=40 \end{gathered}`