How do you solve #abs(5x+2)>=abs(3x-4)#?

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Answer 1 · 2018-03-21T12:10:40

#x le -3# and #x ge 1/4#

This inequality is equivalent to

#sqrt((5x+2)^2) ge sqrt((3x-4)^2)# now squaring both sides

#(5x+2)^2 ge (3x-4)^2# or

#(5x+2)^2 - (3x-4)^2 ge 0# or

#(5x+2-3x+4)(5x+2+3x-4) ge 0# or

#(2x+6)(8x-2) ge 0# or

#(x+3)(x-1/4) ge 0# or

#x le -3# and #x ge 1/4#