Section 2.5

Linear Inequalities in One Variable(Interval Notation)

Definition

• A linear inequality in one variable can be written in the form

baxbaxbaxbax

More…

• Like linear equations, we solve inequalities by isolating the variable.

• For this reason, all the steps from Section 2.1 are valid.

• VERY IMPORTANT: If you multiply or divide by a negative, you MUST reverse your inequality sign.

• However, after you find the solution there are two additional things to do.

1. Graph your solution

• No more open and closed circles!!!!• The open circle has been replaced by the

parenthesis.• The closed circle has been replaced by

the bracket.

2. Write Your Solution in Interval Notation

• Interval notation is another way of expressing the solution to an inequality.

• When we write interval notation we are stating that the numbers in the solution set are between “here” and “there”.

• The table on page 115 summarizes the different types of intervals.

• Remember to use parentheses with both positive and negative infinity.

Practicing Interval Notation

For each inequality below, graph the solution and write the solution in interval notation.

2101

2345

xx

xxxx

Solve, Graph, and Write Your Solution In Interval Notation

)16(25)4(7

)56(32)110(

57

28225.15.2

73

xxx

xx

xxx

x

Compound Inequalities

• Compound inequalities have:1. More than one inequality sign (in which

case we isolate the variable in the middle).

2. The conjunctions “and” or “or” (in which case we solve them separately, then graph according to the conjunction).

Compound Inequalities

8324

34133

811

x

xx