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

Feb 8, 2018

See a step process below;

Explanation:

$2 n - 4 \le - 22$

Adding $4$ to both sides

$2 n - 4 + 4 \le - 22 + 4$

$2 n + 0 \le - 22 + 4$

$2 n \le - 18$

Divide both sides by $2$

$\frac{2 n}{2} \le - \frac{18}{2}$

$\frac{\cancel{2} n}{\cancel{2}} \le - \frac{18}{2}$

$n \le - \frac{18}{2}$

$n \le - 9$

Similarly..

$8 n - 5 \ge - 53$

Adding $5$ to both sides

$8 n - 5 + 5 \ge - 53 + 5$

$8 n + 0 \ge - 53 + 5$

$8 n \ge - 48$

Divide both sides by $8$

$\frac{8 n}{8} \ge - \frac{48}{8}$

$\frac{\cancel{8} n}{\cancel{8}} \ge - \frac{48}{8}$

$n \ge - \frac{48}{8}$

$n \ge - 6$

So we have;

$n \le - 9 \mathmr{and} n \ge - 6$

Therefore;

$n = - 9 , - 10 , - 11 , - 12 \ldots .$

or

$n = - 6 , - 5 , - 4 , - 3 , - 1 \ldots .$

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??

$n \le - 9 \mathmr{and} n \ge - 6$ [separately] (same as the top inequalities)