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:   Multiplying both sides by , and switching the inequality symbol due to multiplication by a negative number:  We do not need to go further. An absolute value expression must always be greater than or equal to 0; it is impossible for the expression to be less than any negative number. The inequality has no solution.

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