Transcript 3.1 - Inequalities and Their Graphs

Vocabulary
Inequality: A mathematical sentence that compares the values of
two expressions using an inequality symbol.
Solution of an inequality: any number that makes the inequality
true.
Example: the solutions of the inequality x < 3, are all numbers
that are less than 3.
Inequalities and Their Graphs
ALGEBRA 1 LESSON 3-1
Is each number a solution of x > 5?
a. –2
No, –2 > 5 is not true.
c. 25
b. 10
5
Yes, 10 > 5 is true.
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Yes, 5 > 5 is true.
Inequalities and Their Graphs
ALGEBRA 1 LESSON 3-1
Is each number a solution of 3 + 2x < 8?
a. –2
b. 3
3 + 2x < 8
3 + 2x < 8
3 + 2(–2) < 8
Substitute for x.
3 + 2(3) < 8
Substitute for x.
3–4<8
Simplify.
3+6<8
Simplify.
–1 < 8
Compare.
9<8
Compare.
–2 is a solution.
3 is not a solution.
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Tip:
Always make sure the variable is on the left before you graph…..
Because……..
Your solutions……..
(are you ready???????)
Will always be……..
in the direction………
your inequality………
is pointing……
****This is why we always SWITCH and FLIP!!!
Graphing Inequalities
Since the solution of an inequality is not just one number, you can use a graph
to indicate all of the solutions.
Inequality
x<3
m > -2
Graph
*The open dot shows that 3 is
not a solution. Shade to the
left of 3.
*The closed dot shows that -2 is a
solution. Shade to the right of -2
*The closed dot shows that -1
is a solution. Shade to the left
of -1.
-1 > a
*switch (variable and number) and flip (inequality) first* will explain on next slide
Inequalities and Their Graphs
ALGEBRA 1 LESSON 3-1
b. Graph –3 ≥ g.
a. Graph d < 3.
The solutions of d < 3 are
all the points to the left of 3.
The solutions of –3 > g are
–3 and all the points to the
left of –3.
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Inequalities and Their Graphs
ALGEBRA 1 LESSON 3-1
Write an inequality for each graph.
x<2
Numbers less than 2 are graphed.
x < –3
Numbers less than or equal to –3 are graphed.
x > –2
Numbers greater than –2 are graphed.
1
x > 2
1
Numbers greater than or equal to
2
are graphed.
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Inequalities and Their Graphs
ALGEBRA 1 LESSON 3-1
Define a variable and write an inequality for each situation.
a. A speed that violates the
law when the speed limit is
55 miles per hour.
b. A job that pays at
least $500 a month.
Let v = an illegal speed.
Let p = pay per month.
The speed limit is 55,
so v > 55.
The job pays $500 or more,
so p > 500.
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Inequalities and Their Graphs
ALGEBRA 1 LESSON 3-1
pages 136–139 Exercises
12. a. yes b. no c. no
24.
2. no
14. a. no
b. no c. yes
26.
4. yes
16. B
6. yes
18. A
8. yes
20.
10. a. yes b. no c. yes
22.
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Inequalities and Their Graphs
ALGEBRA 1 LESSON 3-1
1. Is each number a solution of x > –1?
a. 3 yes
b. –5 no
2. Is 2 a solution of 3x – 4 < 2?
no
3. Graph x > 4.
p < –2
4. Write an inequality for the graph.
5. Graph each inequality.
a. t is at most 2.
b. w is at least 1.
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Answers:
Check your answers and turn in please.
4. Yes
10(a). Yes
12(b). No
14(c). Yes
16. B
20.
O
-3
23. O
-2
28. X ≤ 7
32. X < -1/2
34. a ≥ 16