Bottom half starting from “Given: XY = x + 6”

Problem 22

Explanation:

Segments XY and YZ add up to segment XZ

XY + YZ = XZ

(x+6) + (3x+1) = 5x

4x+7 = 5x

7 = 5x-4x

7 = x

x = 7

Problem 23

Explanation:

We'll use the result in the previous problem to find that,

XY = x+6

XY = 7+6

XY = 13

Problem 24

Explanation:

Similar to problem 23, we'll use the value of x = 7 to find that,

YZ = 3x+1

YZ = 3*7+1

YZ = 21+1

YZ = 22

Problem 25

Explanation:

We have two options. We could add the results of the last two problems

XZ = XY + YZ = 13+22 = 35

Or we could compute XZ directly like so

XZ = 5x = 5*7 = 35

Either way, we get the same result. The fact we get the same value both times helps confirm we have the correct x value and the correct lengths of XY and YZ.

Concept:

Here, we need to know the idea of the segment addition postulate.

The segment addition postulate states the given 2 points A and C, a third point B lies on the line segment AC if and only if the distances between the points satisfy the equation AB + BC = AC. In another word, if 3 points A, B, and C are collinear and B is between A and C, then AB + BC = AC.

If you are still confused, please refer to the attachment below for a graphical explanation.

Solve:

Given information

XY = x + 6

YZ = 3x + 1

XZ = 5x

Given expression deducted according to the segment addition postulate

XY +YZ = XZ

Substitute values into the expression

x + 6 + 3x + 1 = 5x

Combine like terms

4x + 7 = 5x

Subtract 4x on both sides

4x + 7 - 4x = 5x - 4x

x = 7

Find the value of XY

XY = x + 6 = (7) + 6 = 13

Find the value of YZ

YZ = 3x + 1 = 3 (7) + 1 = 22

Find the value of XZ

XZ = 5x = 5 (7) = 35

Check:

Left-hand side: XY + YZ = 13 + 22 = 35

Right-hand side: XZ = 35

35 = 35

Hope this helps!! :)

Please let me know if you have any questions

2500

step-by-step explanation: