-6 < n/9 -5 = Solve each inequality and graph it's solution.

Question

Solve the inequality and graph. 

Answer 1

Without parentheses and brackets to isolate each term, I'm not sure I correctly read your question. 

I think your problem is (-6) < [(n/9)-5].  If yes, then here's how I would solve it:

Treat the inequality sign ( < ) just as you would an equal ( = ) sign.

Get the term with n by itself on:  -6 +5 < n/9, or -1 < n/9

Now multiply both sides by 9 to get n alone:  (-1)(9) < (n/9)(9) or -9 < n

Now you can turn it around - just remember that n is on the "bigger than" side of the <:

n > -9

 

 

Answer 2

Remember, your goal is to isolate the variable by getting all the numbers on the opposite side of the inequality. You can do this by reverse PEMDAS. In this case first, add or subtract, then divide or multiply.

How do you choose which operation to use? Use the "opposite" operation. In this problem, the 5 is subtracted, so to get it to the other side you have to add 5 to each side of the inequality. Next, the problem has n divided by 9. In order to get the n alone, you have to multiple each side by 9. 

You should get n>-9.

Number line graphs: When graphing this, use an open hole because there is no equal sign in the original problem. Shade the part of the line that makes this true. 

Answer 3

Add 5 to both sides,

-1 < n/9

Multiply both sides by 9,

-9 < n

Answer: n > -9.

Can you graph it?