How do you write the inequality and solve "the sum of 3 times a number and 4 is between -8 and 10#?

1 Answer
Jan 16, 2017

Answer:

#-8<3n+4<10 <=> -4 < n < 2#

Explanation:

First off we have the statement "3 times a number plus 4".
Part of the fun of math is variables. It can be any symbol you want to stand for the number. For simplicity I chose the letter n for "number".

So the English statement "3 times a number plus 4" becomes #3n+4#.

Since #3n+4# is "in between -8 and 10" we know that -8 is less than #3n+4# and 10 is greater.

So,

#-8<3n+4#

and

#3n+4<10#

these two statements can be combined into

#-8<3n+4<10#

Now it's time to solve.

#-8<3n+4<10#

#<=>#

#-8-4<3n+4-4<10-4# subtract 4 from each part

#<=>#

#-12<3n<6#

Now we can divide by 3, because it's a common factor

#<=>#

#-4< n < 2#

So now we know that n is between -4 and 2. The inequality is simplified.