How do you solve $abs(2x+9)=abs(7x-2)$ ?

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Answer 1 · 2018-06-26T11:33:01

Solution: $x=11/5, x= -7/9$

$|2 x+ 9| =|7 x- 2|$ . Squaring both sides we get,

$(2 x+ 9)^2 =(7 x- 2)^2$ or

$4 x^2+36 x +81 =49 x^2-28 x +4$ or

$45 x^2- 64 x -77= 0 ; a=45 ,b=-64 ,c=-77$

Discriminant $D= b^2-4a c = 64^2-4*77*45=17956$

Quadratic formula: $x= (-b+-sqrtD)/(2a)$

$:. x= (64+-sqrt 17956)/(2*45)= 32/45 +- 134/90$ or

$x = 32/45 +- 67/45:. x = 99/45=11/5 and x= -35/45=-7/9$

Solution: $x=11/5, x= -7/9$ [Ans]

How do you solve abs(2x+9)=abs(7x-2)abs(2x+9)=abs(7x-2)?