Question

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

Answer 1

Answer:

5. x = -1

6. x = 2

Step-by-step explanation:

5. AB = 5

BC = 2x + 6

AC = x + 10

AB + BC = AC (segment addition postulate)

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

Collect like terms

5 + 6 + 2x = x + 10

11 + 2x = x + 10

2x - x = - 11 + 10

x = -1

6. AB = 9x + 7

BC = -3x + 20

AC = 39

AB + BC = AC (segment addition postulate)

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

Solve for x

9x + 7 - 3x + 20 = 39

Collect like terms

9x - 3x + 7 + 20 = 39

6x + 27 = 39

Subtract 27 from both sides

6x + 27 - 27 = 39 - 27

6x = 12

Divided both sides by 6

6x/6 = 12/6

x = 2