How do you write the inequality and solve "eight less than a number is no more than 14 and no less than 5#?

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Answer 1 · 2017-04-14T13:43:54

See the entire solution process below:

First, let's call "a number": #n#

Then. "eight less than a number" can be written as:

#n - 8#

This expression "is no more than 14" can be written as:

#n - 8 <= 14#

This expression "and no less than 5" can be written as:

#n- 8 >= 5#

Or

#5 <= n - 8#

We can combine these two inequalities as:

#5 <= n - 8 <= 14#

To solve we can add #color(red)(8)# to each segment of the inequality to solve for #n# while keeping the system of inequalities balanced:

#5 + color(red)(8) <= n - 8 + color(red)(8) <= 14 + color(red)(8)#

#13 <= n - 0 <= 22#

#13 <= n <= 22#

Or

#n >= 13# and #n <= 22#

Or

#[13, 22]#