How do you solve #x^2<=4x# using a sign chart?
1 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!