# Solutions to Problem Set 2

Math 101-06

9-6-2017

[Linear inequalities]

1. Solve the inequality for x. Write your answer using either inequality notation or interval notation.

The solution is or .

2. Solve the inequality for x. Write your answer using either inequality notation or interval notation.

3. Solve the inequality for x. Write your answer using either inequality notation or interval notation.

The last inequality is false, because 17 is not less than 14. Hence, the original inequality has no solutions.

You may write your answer as , the symbol for the empty set. Don't write things like "DNE".

4. Solve the inequality for x. Write your answer using either inequality notation or interval notation.

The last inequality is true, because -17 is less than 6. Hence, the original inequality is true for all x.

5. Solve the inequality for x, writing your answer using either inequality notation or interval notation.

The solution is , or .

6. Solve the inequality for x. Write your answer using either inequality notation or interval notation.

The denominators of the fractions are 10, 4, and 2. The least common multiple of 10, 4, and 2 is 20. So I'll multiply both sides by 20 to clear the fractions.

7. Solve the inequality for x. Write your answer using either inequality notation or interval notation.

The denominators of the fractions are 3, 6, and 4. The least common multiple of 3, 6, and 4 is 12. So I'll multiply both sides by 12 to clear the denominators.

8. Solve the inequality for x. Write your answer using either inequality notation or interval notation.

Arriving at one goal is the starting point to another. - John Dewey

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