# GRE Subject Test: Math : Absolute Value Inequalities

## Example Questions

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### Example Question #1 : Absolute Value Inequalities

or

Explanation:

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 #51 : Algebra

or

or

or

or

Explanation:

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 #1 : Absolute Value Inequalities

There is no solution.

and

and

and

and

Explanation:

### Example Question #1 : Absolute Value Inequalities

There is no solution.

There is no solution.

Explanation:

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?

Explanation:

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

### Example Question #6 : Absolute Value Inequalities

and

and

There is no solution.

and

and

Explanation:

and

and

and

and

and

Explanation:

### Example Question #1 : Absolute Value Inequalities

and

and

There is no solution.

and

and

Explanation:

### Example Question #9 : Absolute Value Inequalities

and

There is no solution.

and

and

and

Explanation:

and

and

and

and

and

Explanation: