### All SAT Math Resources

## Example Questions

### Example Question #111 : Equations / Inequalities

Give the solution set of the rational equation

**Possible Answers:**

**Correct answer:**

Multiply both sides of the equation by the denominator :

Rewrite both expression using the binomial square pattern:

This can be rewritten as a linear equation by subtracting from both sides:

Solve as a linear equation:

### Example Question #111 : Algebra

Solve:

**Possible Answers:**

**Correct answer:**

Multiply by on each side

Subtract on each side

Multiply by on each side

### Example Question #1 : Linear / Rational / Variable Equations

Find the solution to the following equation if x = 3:

y = (4x^{2} - 2)/(9 - x^{2})

**Possible Answers:**

3

no possible solution

0

6

**Correct answer:**

no possible solution

Substituting 3 in for x, you will get 0 in the denominator of the fraction. It is not possible to have 0 be the denominator for a fraction so there is no possible solution to this equation.

### Example Question #1 : Linear / Rational / Variable Equations

I. *x* = 0

II. *x* = –1

III. *x* = 1

**Possible Answers:**

I, II, and III

II only

III only

I only

II and III only

**Correct answer:**

I only

### Example Question #2 : Linear / Rational / Variable Equations

**Possible Answers:**

There is no solution

1

–1/2

3

–3

**Correct answer:**

There is no solution

### Example Question #2 : How To Find Out When An Equation Has No Solution

**Possible Answers:**

None of the other answers

**Correct answer:**

A fraction is considered undefined when the denominator equals 0. Set the denominator equal to zero and solve for the variable.

### Example Question #4 : How To Find Out When An Equation Has No Solution

Solve:

**Possible Answers:**

**Correct answer:**

First, distribute, making sure to watch for negatives.

Combine like terms.

Subtract 7x from both sides.

Add 18 on both sides and be careful adding integers.

### Example Question #3 : How To Find Out When An Equation Has No Solution

Solve:

**Possible Answers:**

Infinitely Many Solutions

No Solution

**Correct answer:**

No Solution

First, distribute the to the terms inside the parentheses.

Add 6x to both sides.

This is false for any value of . Thus, there is no solution.

### Example Question #2 : How To Find Out When An Equation Has No Solution

Solve .

**Possible Answers:**

No solutions

**Correct answer:**

No solutions

By definition, the absolute value of an expression can never be less than 0. Therefore, there are no solutions to the above expression.

### Example Question #1 : How To Find Out When An Equation Has No Solution

,

In the above graphic, approximately determine the x values where the graph is neither increasing or decreasing.

**Possible Answers:**

**Correct answer:**

We need to find where the graph's slope is approximately zero. There is a straight line between the x values of , and . The other x values have a slope. So our final answer is .