Question

AC = 22, BC = x + 14, and AB = x + 10.
Find x.​

Answer 1

Hi there! :)

Answer:

`\huge\boxed{x = -1}`

Given:

AC = 22

BC = x + 14

AB + x + 10

AC is equivalent to AB + BC, therefore:

AC = AB + BC

Substitute in the expressions:

22 = (x + 10) + (x + 14)

Combine like terms:

22 = 2x + 24

Subtract 24 from both sides:

-2 = 2x

Divide both sides by 2:

x = -1

Answer 2

Given : AC = 22, BC = x + 14, and AB = x + 10.

`\rule{130}1`

Solution :

`:\implies\sf AB + BC = AC\:\:\:\:\Bigg\lgroup \bf{Segment\: addition\: postulate}\Bigg\rgroup \\\\\\:\implies\sf (x + 10) + (x + 14) = 22\:\:\:\:\Bigg\lgroup \bf{Substitution}\Bigg\rgroup\\\\\\:\implies\sf 2x + 24 = 22\:\:\:\:\Bigg\lgroup \bf{Simplify\:(added\:like\:term)}\Bigg\rgroup\\\\\\:\implies\sf 2x = -2\\\\\\:\implies\sf x = (-2)/(2)\\\\\\:\implies\underline{\boxed{\pink{\sf x = -1}}}`