evaluating algebraic expressions 3-5inequalities use variables and appropriate operations to write...
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Evaluating Algebraic Expressions
3-5 Inequalities
Inequalities
Use variables and appropriate
operations to write inequality.
Evaluating Algebraic Expressions
3-5 Inequalities
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Evaluating Algebraic Expressions
3-5 Inequalities
Vocabulary
inequalityalgebraic inequalitysolution set
Evaluating Algebraic Expressions
3-5 Inequalities
Notice open circles
< less than
> greater than
Inequality Symbols
Evaluating Algebraic Expressions
3-5 Inequalities
Notice colored in circles
≤ less than or equal to
≥ greater than or equal to
Inequality Symbols
Evaluating Algebraic Expressions
3-5 Inequalities
Write an inequality for each situation.
Additional Example 1: Translating Word Phrases into Inequalities
A. There are at least 35 people in the gym.
p ≥ 35
B. The carton holds at most 12 eggs.
e ≤ 12
“At least” means greater than or equal to.
“At most” means less than or equal to.
Let p = the number of people in the gym.
Let e = the number of eggs the carton hold.
Evaluating Algebraic Expressions
3-5 Inequalities
Write an inequality for each statement.
Additional Example 2: Writing Inequalities
A. A number m multiplied by 5 is less than 25.
5m < 25
B. The sum of a number y and 16 is no more than 100.
y + 16 ≤ 100
m 5 < 25
The sum of a number y and 16 is no more than 100
A number m multiplied by 5 is less than 25.
y + 16 ≤ 100
Evaluating Algebraic Expressions
3-5 Inequalities
This open circle shows that 5 is not a solution.
a > 5
The symbols ≤ and ≥ indicate a closed circle.
This closed circle shows that 3 is a solution.
b ≤ 3
Evaluating Algebraic Expressions
3-5 Inequalities
Graph each inequality.
–3 –2 –1 0 1 2 3
A. –1 > y Draw an open circle at –1. The solutions are all values of y less than –1, so shade the line to the left of –1.
B. z ≥ –2
–3 –2 –1 0 1 2 3
Additional Example 3: Graphing Inequalities
12 Draw a closed circle
at –2 and all values of z greater than 2 . So shade to the right of –2 .
1 2 1
2 1 2
Evaluating Algebraic Expressions
3-5 Inequalities
Graph each inequality.
–3 –2 –1 0 1 2 3
A. n < 3
B. a ≥ –4
–6 –4 –2 0 2 4 6
Check It Out! Example 3
Draw an open circle at 3. The solutions are all values of n less than 3, so shade the line to the left of 3.
Draw a closed circleat –4. The solutions are all values greater than –4, so shade to the right of –4.
Evaluating Algebraic Expressions
3-5 Inequalities
Evaluating Algebraic Expressions
3-5 Inequalities
Write a compound inequality for each statement.
Additional Example 4: Writing Compound Inequalities
A. A number x is both less than 4 and greater than or equal to –2.5.
–2.5 ≤ x < 4
B. A number t is either greater than –1 or less than or equal to –7.
t > –1 or t ≤ –7
Evaluating Algebraic Expressions
3-5 Inequalities
Write a compound inequality for each statement.
Check It Out! Example 4
A. A number t is both greater than 9 and less than or equal to 18.5
9 < t 18.5
B. A number y is either greater than –5 or less than or equal to –1.
y > –5 or y ≤ –1
Evaluating Algebraic Expressions
3-5 InequalitiesLesson Quiz: Part I
Write an inequality for each situation.
1. Fewer than 150 people bought tickets.
2. There are at least 20 finches in the cage.
Write an inequality for each statement.
3. A number n decreased by 5 is at most 16.
4. The product of 15 and a number z is greater than 100.
f ≥ 20
p < 150
n – 5 ≤ 16
15z > 100
Evaluating Algebraic Expressions
3-5 InequalitiesLesson Quiz: Part II
6. –3 < y
0º
1 2 3–1–23 –
Graph each inequality.
5. m ≤ 1
– – – 0 1 2 3123