1.7 Linear Inequalities in One Variable

A. Interval Notation vs. Inequality NotationB. Determine whether a value is a solution of

an inequalityC. Solve Linear Inequalities (single and double)

Recall:

• Inequality Notation: x ≥ 3• In words: “all real numbers greater than or

equal to 3”• Graphed on a number line:

• Interval Notation:

Write as an inequality:

• (-3, 5]• (-3, ∞)• [0, 2]• (-∞, 4)• [0, ∞)

B. Determine if x = 3 is a solution to the inequality 5

32 xx

C. Solving Linear Inequalities

IF you multiply (or divide) both sides of an inequality by a NEGATIVE constant, then the sign’s direction REVERSES.•Basic example: -4x > 12

• Before doing these examples, sometimes you can tell if the sign is going to flip just by looking. Sometimes it helps to check that out first. Then you can write “flip” on that one just to remind yourself about the rule.

• With these, can you tell if the sign will flip?

Will these signs flip?

• -3x + 4 < 8• 4x – 8 < 7• 4 – 2x ≥ 1• 8 + 6x > 7• (-3/2)x - 7 <8• But, not so sure about 5x – 7 > 3x + 9 without

working it out.

Solve 5x – 7 > 3x + 9. Put answer in interval notation and graph on a number line.

• Let’s go for getting the x’s on the left and the constant terms on the right.

• 5x – 7 – 3x > 3x + 9 – 3x• 2x – 7 > 9

• 2x > 16

• x > 8

42

31 x

x

53

2 xx

Solve a double Inequality by doing operations to “all 3 sides,” to isolate x. Put in interval notation.

-3 ≤ 6x – 1 < 3

1 < -2x + 3 < 9

52

30

x