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How do you solve the inequality #-n/3 - 5<-4#?

Answer 1

Kennedy Adams

#n > -3#

Add 5 to both sides

#-n/3+0<-4+5#

#-n/3<1#

Multiply both sides by 3

#-n<3# ...............................(1)

Add #n# to both sides

#0 < 3+n#

Subtract 3 from both sides

#-3 < n#

#n > -3# '~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Reconsider inequality (1)

Shortcut method Multiply by (-1) and turn the inequality round the other way

#=>(-1)(-n<3) ->" " n>3#

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Answer 2

Isaiah Anthony

To solve the inequality (-\frac{n}{3} - 5 < -4), follow these steps:

Add 5 to both sides of the inequality:
(-\frac{n}{3} < -4 + 5)
(-\frac{n}{3} < 1)
Multiply both sides by -3 (note: multiplying or dividing both sides of an inequality by a negative number reverses the inequality direction):
(n > 1 \times (-3))
(n > -3)

Therefore, the solution to the inequality is (n > -3).

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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.

How do you solve the inequality #-n/3 - 5&lt;-4#?

How do you solve the inequality #-n/3 - 5<-4#?