Solving Inequalities by the Graphical Method

Exercises for students:
Solve the following problems on paper and check your answers using the above applet:

Solve 2 - x^2 < abs(x-2)
Solve 2 - x^2 > abs(x-2)
Solve x^2 < x
Solve x^2 > x
Solve 1/x < x
Solve 1/x > x
Solve 2x - 1 < abs(x-2)
Solve 2x - 1 > abs(x-2)
Solve abs(2x) < abs(x-3)
Solve abs(2x) > abs(x-3)

Sketch the graph of y = abs(x+2) and hence, or otherwise, solve the inequality 2x + 1 < abs(x+2).

Sketch the graph of y = abs(x+2) and hence, or otherwise, solve the inequality 2x - 1 < abs(x+2).

Sketch, on the same diagram, the graphs of y = 1/x and y = 2x + 1.
Hence, or otheriwse, find the solution set of the inequality 2x + 1 > 1/x.

Sketch, on the same diagram, the graphs of y = 1/x and y = 2x - 1.
Hence, or otheriwse, find the solution set of the inequality 2x - 1 > 1/x.

You can define the inequality using the following operators:

+	-	*	/	^
abs( )	sqrt( )	ln( )	exp( )	pi
	sin( )	cos( )	tan( )
	asin( )	acos( )	atan( )
	sinh( )	cosh( )	tanh( )

Right-click here to download this page, the Java Class File and unzip the Javathings Math Package.
This applet uses the com.javathings.math package developed by:
Patrik Lundin
patrik@javathings.com
http://www.javathings.com