Bell WorkBell Work

VocabularyVocabulary Inequality – a mathematical statement

that shows the relationship between quantities that are not equivalent.

Algebraic Inequality – an inequality that contains at least one variable.

Solution Set – the set of values that make a statement true.

Compound Inequality – a combination of more than one inequality.

These need to be added to your cards (27).

≥

≤

>

<

Word PhrasesMeaningSymbol

is less than

is greater than

is greater than or equal to

is less than or equal to

Fewer than, below

More than, above

At most, no more than

At least, no less than

Symbols you will see with Symbols you will see with Inequalities:Inequalities:

Write an inequality for each situation.

A. There are at least 15 people in the waiting room.

number of people ≥ 15

B. The tram attendant will allow no more than 60 people on the tram.

number of people ≤ 60

“At least” means greaterthan or equal to.

“No more than” meansless than or equal to.

Writing InequalitiesWriting Inequalities

Write an inequality for each situation.

A. There are at most 10 gallons of gas in the tank.

gallons of gas ≤ 10

B. There is at least 10 yards of fabric left.

yards of fabric ≥ 10

“At most” means lessthan or equal to.

“At least” meansgreater than or equal to.

Writing InequalitiesWriting Inequalities

An inequality that contains a variable is an algebraic inequality. A value of the variable that makes the inequality true is a solution of the inequality.

An inequality may have more than one solution. Together, all of the solutions are called the solution set.

You can graph the solutions of an inequality on a number line. If the variable is “greater than” or “less than” a number, then that number is indicated with an open circle.

Graphing InequalitiesGraphing Inequalities

This open circle shows that 5 is not a solution.

a > 5

If the variable is “greater than or equal to” or “less than or equal to” a number, that number is indicated with a closed circle.

This closed circle shows that 3 is a solution.

b ≤ 3

Graph each inequality.

–3 –2 –1 0 1 2 3

A. n < 33 is not a solution, so draw an open circle at 3. Shade the line to the left of 3.

B. a ≥ –4

–6 –4 –2 0 2 4 6

–4 is a solution, so draw a closed circleat –4. Shade the lineto the right of –4.

Let’s Graph These:Let’s Graph These:

Graph each inequality.

–3 –2 –1 0 1 2 3

A. p ≤ 22 is a solution, so draw a closed circle at 2. Shade the line to the left of 2.

B. e > –2

–3 –2 –1 0 1 2 3

–2 is not a solution, so draw an open circleat –2. Shade the lineto the right of –2.

Now You Try!Now You Try!

A compound inequality is the result of combining two inequalities. The words and and or are used to describe how the two parts are related.

x > 3 or x < –1 –2 < y and y < 4

x is either greater than 3 or less than–1.

y is both greater than –2 and less than 4. y is between –2 and 4.

The compound inequality –2 < y and y < 4 can be written as –2 < y < 4.

Writing Math

Compound InequalitiesCompound Inequalities

Graph each compound inequality.

0 1 2 3 4 5 6123456– – – – – –

m ≤ –2 or m > 1First graph each inequality separately.

m ≤ –2 m > 1

Then combine the graphs.

0 2 4 6246– – –•

0 2 4 6–2–4–6º

The solutions of m ≤ –2 or m > 1 are the combined solutions of m ≤ –2 or m > 1.

Graphing Compound Graphing Compound InequalitiesInequalities

Graph each compound inequality

–3 < b ≤ 0–3 < b ≤ 0 can be written as the inequalities–3 < b and b ≤ 0. Graph each inequality separately.

–3 < b b ≤ 0

0 2 4 6246– – –0 2 4 6–2–4–6º •

Then combine the graphs. Remember that –3 < b ≤ 0 means that b is between –3 and 0, and includes 0.

0 1 2 3 4 5 6123456– – – – – –

Graphing Compound Graphing Compound InequalitiesInequalities

–3 < b is the same as b > –3. Reading Math

Hint, Hint!!!Hint, Hint!!!

Exit Ticket:Exit Ticket:Write an inequality for each situation.1. No more than 220 people are in the

theater.

2. There are at least a dozen eggs left.

3. Fewer than 14 people attended the meeting.

number of eggs ≥ 12

people in the theater ≤ 220

people attending the meeting < 14