# 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.

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