Solve for x if |x+2|=|2x+1| ?

2 Answers
sankarankalyanam
Feb 11, 2018

x = 1

Explanation:

x + 2 = 2x + 1

Bring like terms together.

Subtract x from both sides,

x + 2 -cancel x = cancel(2x)^color(red)x + 1 - cancelx

2 = x + 1

Subtract 1 from both sides,

cancel2^color(red)1 - cancel1 = x + cancel1 - cancel1

x = 1

MattyMatty
Feb 11, 2018

x = pm 1

Explanation:

"We could square both sides : "
(x+2)^2 = (2x+1)^2
=> x^2 + cancel(4x) + 4 = 4x^2 + cancel(4x) + 1
=> 3x^2 - 3 = 0
=> x^2 = 1
=> x = pm 1

"The absolute value is > 0 and squaring yields also values > 0."
"So we will have the same solutions."

"We could also work with the definition of |x| : "
={(x " , "x>=0),(-x " , "x<=0):}
"But here we have 4 cases, 2 for the LHS (left hand side of"
"the equation) and 2 for the RHS, so it is a lot of work to deal"
"with 4 cases, squaring is easier."

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