Question

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

Answer 1

The value of $x$ is 4.

By Geometry, we know that line segment $DF = DE + EF$, which is equivalent to:

$DF = 3\cdot x + 2 + x + 5$

$DF = 4\cdot x + 7$ (1)

Now we solve algebraically the resulting expression.

If we know that $DF = 23$, then we solve the equation for $x$:

$4\cdot x + 7 = 23$

$4\cdot x = 16$

$x = 4$

The value of $x$ is 4.

We kindly invite to see this question on line segments: brainly.com/question/23297288