# 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:

$x < \frac{1}{4} \left(3 x + 4\right)$

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

$4 x < 3 x + 4$

Subtract 3x from both sides:
$x < 4$

So any number less than 4 will work!

Sep 19, 2017

n < 4

#### Explanation:

Writing the problem statement as an equation gives:

$n < \frac{1}{4} \left(3 n + 4\right)$

$n < \frac{3}{4} n + 1$
...subtract $\frac{3}{4} n$ from both sides:

$\frac{1}{4} n < 1$

muliply both sides by 4, gives:

$n < 4$

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.