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

Question

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

Julia Adams · Accepted Answer

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

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]}

Isaiah Anthony · Answer

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

Genesis Allen · Answer

undefined To solve the absolute value inequality $|6 - 5y| > 2$, set up two cases: one where $6 - 5y$ is greater than 2, and another where $6 - 5y$ is less than -2. Solve each case separately to find the solution set for $y$.

How do you solve #abs(6 - 5y )&gt;2#?

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