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

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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, $a^2 - b^2 = (a - b)(a + b)$ ,

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

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

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

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

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