### All GRE Subject Test: Math Resources

## Example Questions

### Example Question #1 : Absolute Value Inequalities

**Possible Answers:**

or

**Correct answer:**

The first thing we must do is get the absolute value alone:

When we're working with absolute values, we are actually solving *two* equations:

and

Fortunately, these can be written as one equation:

*If you feel more comfortable solving the equations separately then go ahead and do so.*

*To get alone, we added on both sides of the inequality sign*

### Example Question #1 : Absolute Value Inequalities

**Possible Answers:**

There is no solution.

**Correct answer:**

There is no solution.

Because Absolute Value must be a non-negative number, there is no solution to this Absolute Value inequality.

### Example Question #1 : Absolute Value Inequalities

The weight of the bowling balls manufactured at the factory must be lbs. with a tolerance of lbs. Which of the following absolute value inequalities can be used to assess which bowling balls are tolerable?

**Possible Answers:**

**Correct answer:**

The following absolute value inequality can be used to assess the bowling balls that are tolerable:

### Example Question #4 : Absolute Value Inequalities

**Possible Answers:**

and

and

There is no solution.

and

**Correct answer:**

and

The correct answer is and

### Example Question #1 : Absolute Value Inequalities

**Possible Answers:**

and

and

and

and

**Correct answer:**

and

The correct answer is and

### Example Question #1 : Absolute Value Inequalities

**Possible Answers:**

and

and

and

There is no solution.

**Correct answer:**

and

The correct answer is and

### Example Question #1 : Absolute Value Inequalities

**Possible Answers:**

and

and

and

and

**Correct answer:**

and

The correct answer is and

### Example Question #1 : Absolute Value Inequalities

A type of cell phone must be less than 9 ounces with a tolerance of 0.4 ounces. Which of the following inequalities can be used to assess which cell phones are tolerable? (w refers to the weight).

**Possible Answers:**

**Correct answer:**

The Absolute Value Inequality that can assess which cell phones are tolerable is:

### Example Question #1 : Absolute Value Inequalities

Solve for x:

**Possible Answers:**

**Correct answer:**

Step 1: Separate the equation into two equations:

First Equation:

Second Equation:

Step 2: Solve the first equation

Step 3: Solve the second equation

The solution is

### Example Question #1 : Absolute Value Inequalities

Which of the following expresses the entire solution set of ?

**Possible Answers:**

and

and

**Correct answer:**

Before expanding the quantity within absolute value brackets, it is best to simplify the "actual values" in the problem. Thus becomes:

From there, note that the absolute value means that one of two things is true: or . You can therefore solve for each possibility to get all possible solutions. Beginning with the first:

means that:

For the second:

means that:

Note that the two solutions can be connected by putting the inequality signs in the same order: