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

2 Answers

6 votes

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

User Stevangelista
by
9.4k points
6 votes

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}}}

User Nahomy
by
7.8k points

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