Math CentralQuandaries & Queries


Question from Nunya:

3(4 + 2n) > 2n - 16

Hi Nunya,

You didn't give any instructions but I expect you are to find the values of $n$ for which the inequality is true.

You can work to solve an inequality much as you do to solve an equation, but with one exception. Let's look at a couple of examples.

If the inequality is $4n + 4 > 2(n - 6)$ then you can expand the right side to get $4n + 4 > 2n - 12.$ now add -4 to each side to get $4n > 2n - 16.$ Now add $-2n$ to each side to get $2n > -16.$ finally multiplying both sides by $\large \frac{1}{2}.$ gives $n > -8.$ Hence the given inequality is true if $n > -8.$

Now a second example.

If the inequality is $3n - 6 > 5(n-2).$ Expanding the right side gives $3n - 6 > 5n - 10.$ Now add 6 to each side and the inequality becomes $3n > 5n - 4.$ Now add $-5n$ to each side and you get $-2n > -4.$ Now you need to multiply both sides by $-\large \frac{1}{2}$ but when you multiply both sides of an inequality by a negative number the direction of the inequality reverses. thus the multiplication yields $n < 2.$ Hence the given inequality is true if $n <2.$

Now try your inequality.


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