Question

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

Answer 1

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)