All ACT Math Resources
Example Question #1 : How To Graph A Two Step Inequality
Solve and graph the following inequality:
To solve the inequality, the first step is to add to both sides:
The second step is to divide both sides by :
To graph the inequality, you draw a straight number line. Fill in the numbers from to infinity. Infinity can be designated by a ray. Be sure to fill in the number , since the equation indicated greater than OR equal to.
The graph should look like:
Example Question #2 : How To Graph A Two Step Inequality
Points and lie on a circle. Which of the following could be the equation of that circle?
If we plug the points and into each equation, we find that these points work only in the equation . This circle has a radius of and is centered at .
Example Question #3 : How To Graph A Two Step Inequality
Which of the following lines is perpendicular to the line ?
The key here is to look for the line whose slope is the negative reciprocal of the original slope.
In this case, is the negative reciprocal of .
Therefore, the equation of the line which is perpendicular to the original equation is:
Example Question #4 : How To Graph A Two Step Inequality
Let D be the region on the (x,y) coordinate plane that contains the solutions to the following inequalities:
, where is a positive constant
Which of the following expressions, in terms of , is equivalent to the area of D?