### All ACT Math Resources

## Example Questions

### Example Question #1 : Algebraic Fractions

Find the inverse equation of:

**Possible Answers:**

**Correct answer:**

To solve for an inverse, we switch x and y and solve for y. Doing so yields:

### Example Question #1 : Algebraic Fractions

Find the inverse equation of .

**Possible Answers:**

**Correct answer:**

1. Switch the and variables in the above equation.

2. Solve for :

### Example Question #1 : Algebraic Fractions

When , .

When , .

If varies inversely with , what is the value of when ?

**Possible Answers:**

**Correct answer:**

If varies inversely with , .

1. Using any of the two combinations given, solve for :

Using :

2. Use your new equation and solve when :

### Example Question #1 : Algebraic Fractions

x |
y |

If varies inversely with , what is the value of ?

**Possible Answers:**

**Correct answer:**

An inverse variation is a function in the form: or , where is not equal to 0.

Substitute each in .

Therefore, the constant of variation, , must equal 24. If varies inversely as , must equal 24. Solve for .

### Example Question #31 : Algebraic Fractions

Two numbers and vary inversely, and when . If this is true, what is the value of when ?

**Possible Answers:**

**Correct answer:**

If when , and the variation is direct, then . Using this, we know that if , .

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