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In the diagram below segment DEF is shown(since all three letters are shown, they are collinear). If DE=3x+2, EF= x+5, and DF= 23, algebraically find the value of x

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Xero099idn

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

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