What is the value of x? Justify each step. AC=32 2x 6x+8 ... A B C Drawing not to scale AB + BC = AC a. 2x+6x + 8 =32 b. 8x + 8 =32 c. 8x =24 d. X =3 e.

Step-by-step explanation:

Given:

AC = 32

AB = 2x

BC = 6x+8

A. segment addition postulate:

Segment Addition Postulate states that given points A and C, a third point B lies on the line segment AC if their distances between the points satisfy the expression:

AB + BC = AC.

B. substitution

This property allows you to substitute quantities for each other into an expression as long as those quantities are equal.

2x + 6x + 8 = 32

C. Simplification property of equality

Adding the like variables together on each side of the equality.

8x + 8 = 32

D. Subtraction property of equality

This involves subtracting the same value on both sides of the equality.

8x + 8 - 8 = 32 - 8

8x = 24

E. Division property of equality

Dividing both sides of the equality with a non zero value.

8x/8 = 32/8

x = 3

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