Question

Which inequality has the solution n <5?

A. 4n + 11 > -9
B. 4n + 11 < -9
C. -4n +11 < -9
D. -4n + 11 > -9

(Please show your work:) )

Answer 1

Let's just pick each and solve

4n + 11 > -9

4n > -9 - 11

4n > -20

n > -20/4

n > -5

This does not give the required solution of n < -5

B would give n < -5, this would also not be correct.

Let us try option C

-4n + 11 < -9

-4n < -9 -11

-4n < -20

n > -20/-4 since we divided by -ve, the sign changes.

n > 5 this does not give the answer as well.

-4n + 11 > -9

-4n > -9 -11

-4n > -20

Divide both sides by 4 and the sign changes.

-4n/4 < -20/-4

n < 5

This is the required solution. So option D gives that solution.

Hope this helps.

Answer 2

Not A because:
(Subtract 11 from both sides)
4n > -20
(Divide both sides by 4)
n > -5

Because we have found that dividing the negative number by 4 does not work, we know B is also wrong.

Not C because:
(Subtract 11 from both sides)
-4n < -20
(Divide each side by -4)
(Reverse inequality sign because you are dividing by a negative number)
n > 5

So, it must be D!
Here's why:
(Subtract 11 from both sides)
-4n > -20
(Divide each side by -4)
(Reverse inequality sign because you are dividing by a negative number)
n < 5

Hope this helps!