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Given segment AC and point B that lies on AC, find AB if AC= 19, AB= -14-7x and CB=21+4x

User Simonzack
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Final answer:

To find AB, substitute the given values into the equation AB + CB = AC and solve for x. Then substitute the value of x back into AB to find its length.

Step-by-step explanation:

To find AB, we can use the fact that AB + CB = AC. We know that AC = 19, CB = 21 + 4x, and AB = -14 - 7x. So, we can substitute these values into the equation to solve for x.

AB + CB = AC

-14 - 7x + 21 + 4x = 19

-14 - 7x + 21 + 4x - 19 = 0

-3x - 14 + 21 - 19 = 0

-3x - 12 = 0

-3x = 12

x = -4

Now that we have the value of x, we can substitute it back into either AB or CB to find the length of the segment. Let's substitute it into AB:

AB = -14 - 7(-4)

AB = -14 + 28

AB = 14

User Nellie Danielyan
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