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B is the midpoint of AC. AB= 3(3x-1) and AC=5(2x+2) find X, AB, BC, and AC

B is the midpoint of AC. AB= 3(3x-1) and AC=5(2x+2) find X, AB, BC, and AC-example-1
User MD Iyasin Arafat
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2 Answers

11 votes
11 votes

Answer: x = 2; AB = 15; BC = 15; AC = 30

Explanation:

AB = BC = 3(3x - 1) = 9x - 3

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

AB + BC = AC

(9x - 3) + (9x - 3) = 10x + 10

9x - 3 + 9x - 3 = 10x + 10

18x - 6 = 10x + 10

8x - 6 = 10

8x = 16

x = 2

Plug x = 2 to find AB, BC, and AC.

AC = BC = 3(3x - 1) = 9x - 3 = 9(2) - 3 = 18 - 3 = 15

AC = 5(2x + 2) = 10x + 10 = 10(2) + 10 = 20 + 10 = 30

User RobLabs
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2.7k points
12 votes
12 votes

Answer:

x = 2

Explanation:

AB is given as 3(3x-1) multiply inside the parenthesis with 3

AB = 9x - 3

AC is given as 5(2x+2) multiply inside the parenthesis with 5

AC = 10x + 10

if B is midpoint of AC then AB = BC and AC = AB + BC if we write this equation using the given values

9x - 3 + 9x - 3 = 10x + 10 add like terms

18x - 6 = 10x + 10 transfer like terms to the same side of the equation

18x - 10x = 10 + 6

8x = 16 divide both sides by 8

x = 2 replace x with 2 in given expressions to find the value of each component

User Peter Suwara
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2.9k points