How do you graph and solve #|2x-6|>|x+4|#?

1 Answer
Feb 8, 2017

Answer:

#x < 2/3color(white)("XX")orcolor(white)("XX")x > 10#

(graphed as a number line)
enter image source here

Explanation:

If #abs(2x-6) > abs(x+4)#
then
#color(white)("XXX")(2x-6)^2 > (x+4)^2#

#color(white)("XXX")4x^2-24x+36 > x^2+8x+16#

#color(white)("XXX")3x^2-32x+20 > 0#

#color(white)("XXX")(3x-2)(x-10) > 0#

This can only be true if:
[1] both factors are greater than #0#
#color(white)("XXX")"if " x > 2/3 " "underline("and")" " x > 10rarr x > 10#
or
[2] both factors are less than #0#
#color(white)("XXX")"if " x < 2/3 " "underline("and")" " x < 10 rarr x <2/3#