The value of [tex]x[/tex] is 4.
By Geometry, we know that line segment [tex]DF = DE + EF[/tex], which is equivalent to:
[tex]DF = 3\cdot x + 2 + x + 5[/tex]
[tex]DF = 4\cdot x + 7[/tex] (1)
Now we solve algebraically the resulting expression.
If we know that [tex]DF = 23[/tex], then we solve the equation for [tex]x[/tex]:
[tex]4\cdot x + 7 = 23[/tex]
[tex]4\cdot x = 16[/tex]
[tex]x = 4[/tex]
The value of [tex]x[/tex] is 4.
We kindly invite to see this question on line segments: https://brainly.com/question/23297288
