IJ = 3x - 5
JK = 2x - 1
IK = 3x + 2
IJ + JK = IK segment addition postulate
3x - 5 + 2x - 1 = 3x + 2 substitution
5x - 6 = 3x + 2 simplify (add like terms)
2x - 6 = 2 subtraction property (subtracted 3x from both sides)
2x = 8 addition property (added 6 to both sides)
x = 4 division property (divided both sides by 2)
JK = 2x - 1 = 2(4) - 1 = 8 - 1 = 7
Answer: JK = 7
Using line segments concepts, it is found that the numerical length of segment jk is of 7 units.
-----------------------
[tex]ik = ij + jk[/tex]
The measures are:
[tex]ik = 3x + 2[/tex]
[tex]ij = 3x - 5[/tex]
[tex]jk = 2x - 1[/tex]
-----------------------
Replacing the measures into the equation, we can find x.
[tex]ik = ij + jk[/tex]
[tex]3x + 2 = 3x - 5 + 2x - 1[/tex]
[tex]3x + 2 = 5x - 6[/tex]
[tex]2x = 8[/tex]
[tex]x = \frac{8}{2}[/tex]
[tex]x = 4[/tex]
-----------------------
The numerical length of segment jk is:
[tex]jk = 2x - 1 = 2(4) - 1 = 8 - 1 = 7[/tex]
7 units.
A similar problem is given at https://brainly.com/question/18285191
