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How do you solve and graph #n+2<=-5# and #n+6>=-6#?

Answer 1

Eva Abramson

#-12≤n≤−7#

we solve each inequality separately, n then combine to get the final answer. :) #n+2≤−5# #n≤−5-2# #n≤−7#

#n+6≥−6# #n≥−6-6# #n≥−12#

therefore combining the inequalities, #n≤−7# and #n≥−12#

#-12 ≤n≤−7#

-Sahar ;)

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Answer 2

Nathan Axel

To solve and graph the inequalities (n + 2 \leq -5) and (n + 6 \geq -6), follow these steps:

Solve each inequality for (n).
Graph the solutions on a number line.
Determine the intersection of the solution sets, if any.

Solving (n + 2 \leq -5): [n \leq -5 - 2] [n \leq -7]

Solving (n + 6 \geq -6): [n \geq -6 - 6] [n \geq -12]

Graphing the solutions on a number line: Plot the point -7 and shade to the left to represent (n \leq -7). Plot the point -12 and shade to the right to represent (n \geq -12).

The intersection of these solution sets is the interval from -12 to -7, inclusive.

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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 and graph #n+2&lt;=-5# and #n+6&gt;=-6#?

How do you solve and graph #n+2<=-5# and #n+6>=-6#?