How do you solve #abs(6 - 5y )>2#?

2 Answers
Narad T.
Apr 1, 2018

The solution is #y in ( -oo, 4/5)uu(8/5,+oo)#

Explanation:

There are #2# solutions for absolute values.

#|6-5y|>2#

#6-5y>2# and #-6+5y>2#

#5y<4# and #5y>8#

#y<4/5# and #y>8/5#

The solutions are

#S_1=y in( -oo, 4/5)#

#S_2=y in (8/5,+oo)#

Therefore,

#S=S_1uuS_2#

#=y in ( -oo, 4/5)uu(8/5,+oo)#

graph{(y-|6-5x|)(y-2)=0 [-5.55, 6.934, -0.245, 5.995]}

Jim G.
Apr 1, 2018

#(-oo,4/5)uu(8/5,+oo)#

Explanation:

#"inequalities of the form "|x|>a#

#"always have solutions of the form"#

#x< -a" or "x > a#

#"thus we have to solve 2 inequalities"#

#6-5y < -2" or "6-5y>2#

#color(blue)"first solution"#

#6-5y < -2larr"subtract 6 from both sides"#

#rArr-5y < -8larr"divide both sides by "-5#

#rArry>8/5larrcolor(blue)"reverse direction of sign"#

#color(blue)"second solution"#

#6-5y>2larr"subtract 6 from both sides"#

#rArr-5y> -4larr"divide both sides by " -5#

#y< 4/5larrcolor(blue)"reverse direction of sign"#

#"combining the solutions gives"#

#(-oo,4/5)uu(8/5,+oo)#

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