# A number is less than one fourth the sum of three times the number and four. What is the number?

##### 2 Answers

Sep 19, 2017

The number is less than 4.

#### Explanation:

If we write the inequality out, we get this:

Now we just need to solve for x. Multiplying both sides by 4 yields:

Subtract 3x from both sides:

So any number less than 4 will work!

Sep 19, 2017

n < 4

#### Explanation:

Writing the problem statement as an equation gives:

...subtract

muliply both sides by 4, gives:

when possible, sanity check your work. For example, if n < 3, does that satisfy the inequality?

#1/4*(9+4) = 1/4(13) =3.25, and 3 is less than that. So, this checks.

How about 5? 5 should NOT satisfy the inequality.

#1/4(15+4) = 1/4(19) = 4.75, and 5 is greater than this, so this checks out too.