How do you solve #abs(5x+4) =abs(2x+5)#?

Question

1617 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2015-04-03T21:54:59

Answers: #x = 1/3# , #x = -9/7#

#|5x + 4| = |2x + 5|#

Squaring both sides of the equation you get,

#(5x + 4)^2 = (2x + 5)^2#

#=> (5x + 4)^2 -(2x + 5)^2 = 0#

Using the idea that, #a^2 - b^2 = (a - b)(a + b)# ,

#=> (5x + 4 -(2x + 5))(5x + 4 + 2x + 5)) = 0#

#=> (3x - 1)(7x + 9) = 0#

#=> 3x - 1 = 0 => x = 1/3#

# 7x + 9 = 0 => x = -9/7#