### 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 #2 : Absolute Value Inequalities

**Possible Answers:**

or

or

or

**Correct answer:**

or

Since the absolute value with x in it is alone on one side of the inequality, you set the expression inside the absolute value equal to both the positive and negative value of the other side, 11 and -11 in this case. For the negative value -11, you must also flip the inequality from less than to a greater than. You should have two inequalities looking like this.

and

Add 5 to both sides in each inequality.

and

Divide by -4 to both sides of the inequality. Remember, dividing by a negative will flip both inequality symbols and you should have this.

and

### Example Question #3 : Absolute Value Inequalities

**Possible Answers:**

There is no solution.

and

and

and

**Correct answer:**

and

The correct answer is and

### Example Question #4 : 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 #5 : 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 #6 : Absolute Value Inequalities

**Possible Answers:**

There is no solution.

and

and

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 #8 : Absolute Value Inequalities

**Possible Answers:**

and

There is no solution.

and

and

**Correct answer:**

and

The correct answer is and

### Example Question #9 : Absolute Value Inequalities

**Possible Answers:**

and

There is no solution.

and

and

**Correct answer:**

and

The correct answer is and

### Example Question #10 : Absolute Value Inequalities

**Possible Answers:**

and

and

and

and

**Correct answer:**

and

The correct answer is and

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