### All PSAT Math Resources

## Example Questions

### Example Question #71 : Equations / Inequalities

Solve for :

**Possible Answers:**

**Correct answer:**

Begin by moving all of the values to the left side of the inequality:

becomes

Next, move the to the right side:

Finally, divide both sides by :

### Example Question #72 : Equations / Inequalities

Solve for :

**Possible Answers:**

**Correct answer:**

First, move the values to the left side of the inequality:

becomes

Next, move the to the right side:

Finally, divide by . Remember:** **you must flip the inequality sign when you multiply or divide by a negative number.

### Example Question #73 : Equations / Inequalities

Solve for :

**Possible Answers:**

**Correct answer:**

First, get the factors on the left side of the inequality:

becomes

Next, subtract from both sides:

Now, divide by . Remember: Dividing or multiplying by a negative number requires you to flip the inequality sign:

### Example Question #74 : Equations / Inequalities

Solve the inequality

**Possible Answers:**

**Correct answer:**

First, multiplying each side of the equality by gives . Next, dividing each side of the inequality by will solve for ; .

### Example Question #1937 : Sat Mathematics

What is the solution set of the inequality ?

**Possible Answers:**

**Correct answer:**

We simplify this inequality similarly to how we would simplify an equation

Thus

### Example Question #1938 : Sat Mathematics

What is a solution set of the inequality ?

**Possible Answers:**

**Correct answer:**

In order to find the solution set, we solve as we would an equation:

Therefore, the solution set is any value of .

### Example Question #5 : How To Find Out When An Equation Has No Solution

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

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

**Possible Answers:**

no possible solution

3

6

0

**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 #2 : Equations / Inequalities

I. *x* = 0

II. *x* = –1

III. *x* = 1

**Possible Answers:**

I only

I, II, and III

II and III only

III only

II only

**Correct answer:**

I only

### Example Question #6 : How To Find Out When An Equation Has No Solution

**Possible Answers:**

–1/2

1

–3

There is no solution

3

**Correct answer:**

There is no solution

### Example Question #7 : 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.

Certified Tutor