SOLUTION: Solve each inequality and graph its solution. 5-6|8n+8|>-91 Thanks!

Question 1122800: Solve each inequality and graph its solution. 5-6|8n+8|>-91 Thanks!
Found 3 solutions by solver91311, ikleyn, MathTherapy:
Answer by solver91311(24713)   (Show Source): You can put this solution on YOUR website!

Note change of sense when multiplying by a negative number.

Hence:

or

Both reduce to:

Note dashed line indicating that the line is NOT included in the solution set.

John

My calculator said it, I believe it, that settles it

Answer by ikleyn(52794)   (Show Source): You can put this solution on YOUR website!
.

5 - 6|8n+8| > -91 ====> add 6|8n+8| to both sides ====> 5 > -91 + 6|8n+8| ====> add 91 to bot sides 5 + 91 > 6|8n+8| ====> rewrite it in this form 6|8n+8| < 96 ====> divide both sides by 6 ====> |8n+8| < 16 ====> equivalent to 8*|n+1| < 16 ====> divide both sides by 8 ====> |n+1| < 2 ====> is equivalent to |n - (-1)| < 2 ====> the solutions to the last inequality are those values of n that are remoted from (-1) to the distance less than 2, i.e. (-1) - 2 < n < (-1) + 2, which is equivalent to - 3 < n < 1. It is your ANSWER: - 3 < n < 1, or, in the interval notation, the interval set (-3,1).

Solved.

Any other solution is incorrect.

The plot below visualize the solution for you.

Plot y = |x+1| (red) and y = 2 (green).

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On solving inequalities, see introductory lessons
    - Solving simple and simplest linear inequalities
    - Solving absolute value inequalities (*)
in this site.   Especially lesson (*) of these two.

Answer by MathTherapy(10552)   (Show Source): You can put this solution on YOUR website!

Solve each inequality and graph its solution. 5-6|8n+8|>-91 Thanks!

Solution set:
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