Question

Use the figure to write the segment addition postulate, write an equation and solve for x.

Answer 1

The calculated values of x in the line segments are x = -1 and x = 2, respectively

How to write an equation and solve for x.

From the question, we have the following parameters that can be used in our computation:

The figures

Using the segment addition postulate, we have

5 + 2x + 6 = x + 10

Solving for x, we have

x = 10 - 6 - 5

x = -1

Next, we have

9x + 7 - 3x + 20 = 39

So, we have

6x = 12

Divide both sides of the equation by 6

x = 2

Hence, the values of x are x = -1 and x = 2

Answer 2

5). x = -1

6). x = 2

Explanation:

5). AC = (x + 10)

AB = 5

BC = (2x + 6)

By segment addition postulate,

AC = AB + BC

(x + 10) = 5 + (2x + 6)

x + 10 = 2x + 11

2x - x = 10 - 11

x = -1

6). AC = 19

AB = 9x + 7

BC = -3x + 20

By segment addition postulate,

AC = AB + BC

39 = 9x + 7 + (-3x + 20)

39 = (9x - 3x) + (7 + 20)

39 = 6x + 27

6x = 39 - 27

6x = 12

x = 2

x = 2