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If AB= x+4, BC=2x-10, and AC=2x+1, then find the value for x

User Wolfy
by
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1 Answer

2 votes

Answer:


\boxed{x = 7}

Explanation:

Given:

  • AB = x + 4
  • BC = 2x – 10
  • AC = 2x + 1

We can illustrate this relationship as:

(2x + 1)

___↑___

| |

A — B — C

|____|___|

↓ ↓

(x + 4) (2x – 10)

_______________________________

When you are given an algebraic expression for the length of a segment, you can solve for that value by knowing that the sum of two segments AB + BC = AC.

Thus:

(x + 4) + (2x – 10) = (2x + 1)

[Regroup terms]

(x + 2x) + (4 – 10) = (2x + 1)

[Simplify]

(3x – 6) = (2x + 1)

[subtract 2x from both sides to isolate the variable]

(3x – 6) – 2x = (2x + 1) – 2x

[Regroup terms]

(3x – 2x) – 6 = (2x – 2x) + 1

x – 6 = 1

[Add 6 to both sides to isolate the constant]

x – 6 + 6 = 1 + 6

[Simplify]

x = 7

User Yousra
by
8.3k points

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