Question

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

Answer 1

`-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.