How do you solve and graph #2n-4<=-22# or #8n-5>=-53#?

1 Answer
Feb 8, 2018

Answer:

See a step process below;

Explanation:

#2n - 4 <= - 22#

Adding #4# to both sides

#2n - 4 + 4 <= - 22 + 4#

#2n + 0 <= - 22 + 4#

#2n <= -18#

Divide both sides by #2#

#(2n)/2 <= -18/2#

#(cancel2n)/cancel2 <= -18/2#

#n <= - 18/2#

#n <= -9#

Similarly..

#8n - 5 >= - 53#

Adding #5# to both sides

#8n - 5 + 5 >= - 53 + 5#

#8n + 0 >= - 53 + 5#

#8n >= - 48#

Divide both sides by #8#

#(8n)/8 >= - 48/8#

#(cancel8n)/cancel8 >= - 48/8#

#n >= - 48/8#

#n >= - 6#

So we have;

#n <= -9 or n >= - 6#

Therefore;

#n = -9, -10, -11, -12 ....#

or

#n = -6, -5, -4, -3, -1 ....#

Note that there are no values which are a solution for BOTH inequalities....

That is the reason for the use of the word 'or' rather than 'and'.

On a number line graph you would have the following:

Two separate parts of the graph:

  • A line with a closed (full) circle on #-9# and extending to the left to negative infinity.

  • A line with a closed (full) circle on #-6# and extending to the right to positive infinity.

A value from either of these will be a possible solution for one of the inequalities given.

Can someone help me to plot these two graphs??

#n <= -9 or n >= - 6# [separately] (same as the top inequalities)