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Notes Algebra Section 3.1 Date_______Writing and Graphing Inequalities

INEQUALITY: A mathematical sentence that compares expressions. I contains the

symbols _<_, >__, __≤_, or __≥_.

To write an inequality, look for the following phrases to determine where to place the inequality symbol

Symbol < > ≤ ≥KeyPhrases Is less than

Is fewer than

Is greater than

Is more than

Is less than or equal to

Is at most

In no more than

Is greater than or equal to

Is at least

Is no less than

EX1) Writing an Inequality: A number w minus 3.5 is less than or equal to -2.w - 3.5 ≤ -2

You try: Write on your whiteboard first, when it is correct, write it in your notes. Write the word sentence as an inequality

● A number b is fewer than 30.4 ___b < 30.4_____

● Twice a number k is at least - 7/10______________2k ≥ -7/10 _____________

A _solution_ of an inequality is a value that makes the inequality true. An inequality can (and usually will) have more than one solution. The set of all the solutions of an inequality is called the __solution set___.

Value of x x + 5 ≥ -2 Is the inequality

true?

-6 -6 + 5 ≥ -2-1 ≥ -2

Yes

-7 -7 + 5 ≥ -2-2 ≥ -2

Yes

-8

⅄

-8 + 5 ≥ -2-3 -2

No

EX2) Checking Solutions Tell whether -4 is a solution of an inequality.

a) x + 8 < -3 b) -4.5x > -21 -4 + 8 < -3 -4.5 (-4) > -21 4 < -3 NO 18 > -21 YES

You try: Write on your whiteboard first, when it is correct, write it in your notes. Tell whether -6 is solution of the following inequalities:

1. c + 4 < -1 2. 5 - m ≤ 10 3. 21 ÷ x ≥ -3.5 YES NO YES

The _graph_ of an inequality shows all the solutions of the inequality on a number line. An _open circle O_is used when a number is NOT a solution. A _closed circle ⬤_is used when a number IS a solution. An arrow to the left or right shows that the graph continues in that direction.

EX3) Graphing an InequalityGraph y ≤ -3

You try: Write on your whiteboard first, when it is correct, write it in your notes. Graph the inequality on a number line.

1. b > -8 2. g ≤ 1.4

3. r < -½ 4. v ≥