### All SAT II Math II Resources

## Example Questions

### Example Question #2 : Absolute Value

Solve .

**Possible Answers:**

**Correct answer:**

First we need to isolate the absolute value term. We do with using some simple algebra:

Now we solve two equations, one with the right side of the equation positive, one negative. Let's start with the positive:

And now the negative:

So our answers are:

### Example Question #2 : Absolute Value

Solve .

**Possible Answers:**

No solutions

**Correct answer:**

No solutions

First, we have to isolate the absolute value:

Let's take a look at our equation right now. It's saying that the absolute value has to be a negative number, which isn't possible. So no solutions exist.

### Example Question #1 : Absolute Value

Solve .

**Possible Answers:**

No solutions

**Correct answer:**

First, we need to isolate the absolute value:

Because the equation is set equal to , we can drop the absolute value symbols and solve normally:

### Example Question #11 : Absolute Value

Solve:

**Possible Answers:**

**Correct answer:**

Add 3 on both sides.

Divide by 25 on both sides.

Recall that an absolute value cannot have a negative value. There is no x-value that will equal to the right term.

The answer is:

### Example Question #12 : Absolute Value

Solve: .

**Possible Answers:**

or

**Correct answer:**

Because the absolute value term is "less than" the other side of the equation, we can rewrite the problem like this:

This eliminates the absolute value. Remember, when an operation is performed, it must be performed on all three sets of terms. When we add to each side, we end up with:

### Example Question #71 : Sat Subject Test In Math Ii

Solve:

**Possible Answers:**

or

**Correct answer:**

or

Here, we have to split the problem up into two parts:

and

Let's start with the first equation:

First, we can add to each side:

Now we divide by -6. Remember, when you divide by a negative, you flip the sign of the inequality:

Which we can reduce:

Now let's do the other part of the problem the same way:

### Example Question #11 : Absolute Value

Give the solution set of the inequality:

**Possible Answers:**

All real numbers

**Correct answer:**

All real numbers

To solve an absolute value inequality, first isolate the absolute value expression, which can be done here by subtracting 35 from both sides:

There is no need to go further. The absolute value of any number is always greater than or equal to 0, so, regardless of the value of ,

.

Therefore, the solution set is the set of all real numbers.

### Example Question #51 : Mathematical Relationships

Solve the absolute value:

**Possible Answers:**

**Correct answer:**

Subtract 2 from both sides.

Under this condition, there are no values of that will give a negative 14.

The answer is:

### Example Question #73 : Sat Subject Test In Math Ii

Solve:

**Possible Answers:**

**Correct answer:**

The lines on the outside of this problem indicate it is an absolute value problem. When solving with absolute value, remember that it is a measure of displacement from 0, meaning the answer will always be positive.

For this problem, that gives us a final answer of 7.

### Example Question #12 : Absolute Value

Solve:

**Possible Answers:**

**Correct answer:**

The lines on the outside of this problem indicate it is an absolute value problem. When solving with absolute value, remember that it is a measure of displacement from 0, meaning the answer will always be positive.

For this problem, that gives us a final answer of 1.

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