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How do you solve and graph #3n ≤ 9#?

Answer 1

Kennedy Adams

See a solution process below:

Divide each side of the inequality by #color(red)(3)# to solve for #n# while keeping the inequality balanced:

#(3n)/color(red)(3) <= 9/color(red)(3)#

#(color(red)(cancel(color(black)(3)))n)/cancel(color(red)(3)) <= 3#

#n <= 3#

To graph this we will draw a vertical line at #3# on the horizontal axis.

The line will be a solid line because the inequality operator contains an "or equal to" clause.

We will shade to the left side of the line because the inequality operator also contains a "less than" clause:

graph{x<= 3 [-10, 10, -5, 5]}

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Answer 2

Genesis Allen

To solve the inequality (3n \leq 9), you divide both sides by 3 to isolate (n):

[ \frac{3n}{3} \leq \frac{9}{3} ] [ n \leq 3 ]

Now, to graph this inequality on a number line, you draw a solid dot at 3 to represent the inclusive inequality (≤), and shade the area to the left of 3 to indicate all the values of (n) that satisfy the inequality.

    <------------------●-----
          n ≤ 3

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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.