# SAT Math : Inequalities

## Example Questions

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### Example Question #1 : Inequalities

What is the solution set of the inequality  ?

Explanation:

We simplify this inequality similarly to how we would simplify an equation

Thus

### Example Question #6 : Inequalities

What is a solution set of the inequality ?

Explanation:

In order to find the solution set, we solve  as we would an equation:

Therefore, the solution set is any value of .

### Example Question #1 : How To Find The Solution To An Inequality With Division

Which of the following could be a value of , given the following inequality?

Explanation:

The inequality that is presented in the problem is:

Start by moving your variables to one side of the inequality and all other numbers to the other side:

Divide both sides of the equation by . Remember to flip the direction of the inequality's sign since you are dividing by a negative number!

Reduce:

The only answer choice with a value greater than  is .

### Example Question #42 : Inequalities

If  and , which of the following gives the set of possible values of ?

Explanation:

To get the lowest value, you need the lowest numerator and the highest denominator.  That would be  or reduced to be .  For the highest value, you need the highest numerator and the lowest denominator.  That would be  or .

### Example Question #43 : Inequalities

Give the solution set of this inequality:

The inequality has no solution.

Explanation:

The inequality  can be rewritten as the three-part inequality

Isolate the  in the middle expression by performing the same operations in all three expressions. Subtract 32 from each expression:

Divide each expression by , switching the direction of the inequality symbols:

This can be rewritten in interval notation as .

### Example Question #44 : Inequalities

Give the solution set of this inequality:

The inequality has no solution.

The inequality has no solution.

Explanation:

In an absolute value inequality, the absolute value expression must be isolated first, as follows: