Point B is on line segment \overline{AC} AC . Given AB=2x+10,AB=2x+10, BC=x,BC=x, and AC=5x,AC=5x, determine the numerical length of \overline{AC}. AC

Answer 1

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A. B. C

The ENTIRE line segment from point A to point C has a length equal to 5x.

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A B

This portion of segment AC, which is a smaller segment, AB, has a length equal to 2x + 10.

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B. C

This portion of segment AC, which is a smaller segment, BC, has a length equal to x.

When we take the lengths of the 2 smaller segments, AB & BC, and add them together, the result will be the length of the entire segment, AC. So.......

. AB + BC = AC

Length of AB = 2x + 10

Length of BC = x. So ...... Length of AC = 2x + 10 + x

We also know that the length of AC = 5x

Therefore, 2x + 10 + x = 5x

NOW, SOLVE FOR X.

2x + 10 + x = 5x

3x + 10 = 5x

-3x. -3x

10 = 2x

÷2 ÷2

X = 5

Plug that value (5) in for "x" in the expression that each segment length.

AC = 2x + 10

= 2(5) + 10

AC = 20

BC = x

= (5), so length of segment BC is 5

When you add those 2 lengths together, you should get a result that is equal to the sum of the 2 parts. (20 + 5 = 25)

AC = 5x

= 5(5)

AC = 25

Answer 2

Point B is on line segment \ overline AC . Given AB=2x+10, BC=x, and AC=5x, determine the numerical length of \ overline AC= ??

Detailed Solution:

AB = 2x + 10 BC = x AC = 5x

A======================================================B==============C

AC = AB + BC

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

5x = 3x + 10

5x – 3x = 10

2x = 10

x = 5

Therefore:

AB = 2x + 10 ==> AB = 2(5) + 10 ==> AB = 10 + 10 ==> AB = 20

BC = x ==> BC = (5) ==> BC = 5

AC = 5x ==> AC = 5(5) ==> AC = 25

Check: AC = AB + BC ==> 25 = 20 + 5 ==> 25 = 25