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How do you solve #-5abs(4y-11)-3=12#?

Answer 1

The solution of #x# is #[7/4,2]#

This is an Inequatlity problem. The general forms is: #abs(x-a)=b# #-b<=(x-a)<=b# #(a-b)<=x<=(a+b)# Thus, #x# has a solution range #[#(a-b)#,#(a+b)#]#

The following is how this issue is resolved:

#-5abs(4y-11)-3=12# ;or #-5abs(4y-11)=15# ;or #abs(4y-11)=-3# ;or #-(-3)<=4y-11<=-3# ;or #(11+3)<=4y<=(11-3)# ;or #14<=4y<=8# ;or #7/4<=y<=2# Thus, the solution range of #x# is #[7/4,2]#

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Answer 2

Savannah Anderson

No solution.

#-5|4y-11|-3=12# can be written as

#-5|4y-11|=12+3=15#

or #|4y-11|=15/-5=-3#

There is no answer because a number's absolute value cannot be negative.

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Answer 3

Julia Adams

To solve the equation -5|4y - 11| - 3 = 12, first, add 3 to both sides to isolate the absolute value term. Then, divide both sides by -5. Finally, solve for y by considering both positive and negative cases when removing the absolute value.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.