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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