# How do you solve #x^2<=4x# using a sign chart?

##### 1 Answer

#### Answer:

Move every term to one side, factor the expression, and determine when each factor is

#### Explanation:

This is now written as the product of two factors,

So we have three intervals to examine: below 0, between 0 and 4, and above 4.

A sign chart can be made like this:

. . . . . . . . . .---------0----------4-----------

. . . . . . . . . .----------------------------------

Fill in the sign chart with + and - signs to reflect where each factor is

. . . . . . . . . .---------0---------4-----------

. . . . . . . . . .----------------------------------

To complete the bottom row of the sign chart, each interval is filled with the product of all the signs above it. For example, when

. . . . . . . . . .---------0--------4-----------

. . . . . . . . . .----------------------------------

This tells you that

The solution is

Or

Go ahead and try some values for yourself: say

Which is true!