Solving Inequalities in One Variable

Questions
1. Replace the ? with either < or > in −3 ? − 6.
2. Replace the ? with either < or > in .
3. Graph the inequality on a number line x ≤ -5.3.
4. Graph the inequality on a number line x > −3.5.
5. Translate the graph to an inequality:

6. Suppose that the variable x must satisfy all of these conditions: .
Graph on a number line the region that satisfies all these conditions.
7. Solve and graph the result −4 + 5x < −3x + 8.
8. Solve and graph the result .
9. To pass a course with a B grade, a student must have an average of 80 or greater. A student’s grade on three tests are
75, 83, and 86. Solve the inequality to find out what score the student must get on the final test
to get a B average or better.

Solutions
1. −3 > −6

2. To compare fractions , we need a common denominator. The common denominator is 40.


So we see

3

4.

5. x ≤ 35.

6. The best way to solve this is to stack the graphs of the inequalities and identify the region of overlap. From the sketch
below we see that all the inequalities are satisfied if

7.
add 4 to each side
simplify
add 3x to each side
simplify
multiply both sides by 1/8, direction does not change since we multiplied by positive number

8.

since we are multiplying by a negative number , change direction of inequality.

9.