### All ACT Math Resources

## Example Questions

### Example Question #1 : How To Graph A Two Step Inequality

Solve and graph the following inequality:

**Possible Answers:**

**Correct answer:**

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?

**Possible Answers:**

**Correct answer:**

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 ?

**Possible Answers:**

**Correct answer:**

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 #1 : 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*?

**Possible Answers:**

**Correct answer:**

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