### All SAT II Math II Resources

## Example Questions

### Example Question #31 : Single Variable Algebra

Solve .

**Possible Answers:**

**Correct answer:**

Remember, anything we do to one side of the inequality, we must also do to the other two sides. We can start by adding one to all three sides:

And now we divide each side by two:

### Example Question #32 : Single Variable Algebra

Solve .

**Possible Answers:**

**Correct answer:**

The first thing we can do is distribute the negative sign in the middle term. Because we're not multiplying or dividing the entire inequality by a negative, we don't have the change the direction of the inequality signs:

Now we can subtract from the inequality:

And finally, we can multiply by . Note, this time we're multiplying the entire inequality by a negative, so we have to change the direction of the inequality signs:

### Example Question #33 : Single Variable Algebra

Solve .

**Possible Answers:**

**Correct answer:**

We start by distributing the :

Now we can add , and subtract an from each side of the equation:

We didn't multiply or divide by a negative number, so we don't have to reverse the direction of the inequality sign.

### Example Question #14 : Solving Inequalities

What is the solution set for ?

**Possible Answers:**

**Correct answer:**

Start by finding the roots of the equation by changing the inequality to an equal sign.

Now, make a number line with the two roots:

Pick a number less than and plug it into the inequality to see if it holds.

For ,

is clearly not true. The solution set cannot be .

Next, pick a number between .

For ,

is true so the solution set must include .

Finally, pick a number greater than .

For ,

is clearly not the so the solution set cannot be .

Thus, the solution set for this inequality is .

### Example Question #34 : Single Variable Algebra

Give the solution set of the inequality:

**Possible Answers:**

**Correct answer:**

First, find the zeroes of the numerator and the denominator. This will give the boundary points of the intervals to be tested.

;

Since the numerator may be equal to 0, and are included as solutions. However, since the denominator may not be equal to 0, is excluded as a solution.

Now, test each of four intervals for inclusion in the solution set by substituting one test value from each:

Let's test :

This is false, so is excluded from the solution set.

Let's test :

This is true, so is included in the solution set.

Let's test :

This is false, so is excluded from the solution set.

Let's test :

This is true, so is included in the solution set.

The solution set is therefore .

### Example Question #35 : Single Variable Algebra

Solve the inequality:

**Possible Answers:**

**Correct answer:**

Add 6 on both sides.

Divide by five on both sides.

The answer is:

### Example Question #36 : Single Variable Algebra

Solve the inequality:

**Possible Answers:**

**Correct answer:**

Add six on both sides.

Divide by three on both sides.

The answer is:

### Example Question #41 : Single Variable Algebra

Solve the inequality:

**Possible Answers:**

**Correct answer:**

Subtract nine from both sides.

Divide by negative 3 on both sides. We will need to switch the sign.

The answer is:

### Example Question #42 : Single Variable Algebra

Solve the inequality:

**Possible Answers:**

**Correct answer:**

Add seven on both sides.

Divide by three on both sides.

The answer is:

### Example Question #43 : Single Variable Algebra

Solve:

**Possible Answers:**

**Correct answer:**

First, we distribute the through the equation:

Now, we collect and combine terms: