Download Solving Inequalities

1-5
Solving Inequalities
Vocabulary
Review
1. Write I if the math sentence is an inequality. Write E if it is an equation.
I 15 . 32x
I 45 , 46
I 227 2 3x
E 17x 5 34
Complete each statement with ,, ., or 5.
9
2. 2 S 4
4. 0.6 5 23
3. 5(2 1 3) R 27
5. 26 R 4
Vocabulary Builder
com p oun d in e q uality
com pound (noun)
KA H M
pound
x 7 or x 5
D efinition: A compou nd is made u p of separate parts.
Exam ple: A compou nd inequ ality is made u p of tw o or more simple inequ alities
joined by and or or.
U se Your Vocabulary
6. A stu dent u ses the w ord com pound in three different sentences. P lace a ✓ next to
the sentences that u se the w ord correctly. P lace an ✗ next to those that do not.
✓
In chemistry class w e learn abou t variou s chemicalcom pounds.
✓
C om pound inequ alities contain more than one inequ ality symbol.
✗
To simplify an expression,you can com pound like terms.
W rite an inequality for each verbal d escription.
7. x is at most 25
x K 25
Chapter 1
8. x is not equ alto 25
9. x is greater than 25
x u 25
x S 25
18
10. x is less than 25
x R 25
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Related W ords: compou nd inequ ality,less than,
greater than
P rob lem 1
Writing an Inequality From a Sentence
G ot It? What inequality represents the sentence The quotient of a number and
3 is no more than 15?
11. Circle the expression that represents the phrase “the quotient of a number and 3.”
n23
3
n
n
3
3n
12. T he symbol , > . > $ > # represents the phrase “no more than”.
13. N ow w rite the inequality.
n
3
P rob lem 2
K 15
Solv ing and G rap h ing an Inequality
G ot It? What is the solution of 22(x 1 9) 1 5 L 3? G raph the solution.
14. Solve the inequality for x.
22(x 1 9) 1 5 L 3
22x 2 18 L 22
22x L 16
x K 28
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15. U nderline the correct w ord or number to complete each sentence.
T he graph includes all numbers less / greater than 28 / 22 / 3 / 5 / 9 / 10 .
T he graph w ill include a closed / an open circle at 28 / 22 / 3 / 5 / 9 / 10 .
16. G raph the solution.
0
10 9 8 7 6 5 4 3 2 1
P rob lem 3
1
2
3
4
5
6
7
8
9
10
U sing an Inequality
G ot It? A d igital m usic service offers tw o sub scription plans.T he first has a $9
m em b ership fee and charges $1 per d ow nload .T he second has a $25 m em b ership
fee and charges $.50 per d ow nload .H ow m any songs m ust you d ow nload for the
second plan to cost less than the first plan?
17. D efine the variables. A n sw ers m ay vary. Sam p le:
Let r
5 the number of songs dow nloaded.
Let C1 5 cost of the first plan.
Let C2 5 co st o f th e seco n d p lan
.
19
Lesso n 1-5
Write an algebraic expression to describe the cost of the first plan and the cost of the
second plan.
9 11 r
18. C1 5
19. C2 5 25 1 0.5 r
20. W rite an in equ ality to represen t th e situ ation .T h en solve.
25 1 0.5r R 9 1 r
16 R 0.5r
32.6 R r
21. You m u st dow n load 33 son gs for th e secon d plan to cost less than th e first plan .
N o Solution or A ll R eal N um b ers as Solution
P rob lem 4
G ot It? Is 4(2x 2 3) R 8(x 1 1) a lw a ys,som etim es,or n ever true?
22. C om plete the solution.
4(2x 2 3) , 8(x 1 1)
W rite the original inequality.
8x 2 12 R 8x 1 8
D istributive P roperty
8x 2 20 R 8x
Subtract 8 from each side.
220 R 0
Subtract 8x from each side.
23. T he inequality is alw ays / som etim es / never true.
Th e set o f all real n u m b ers.
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Solving an And Inequality
P rob lem 5
G ot It? What is the solution of 8 K 3x 2 1and 2x R 12? Graph the solution.
25. Solve each inequality.
8 K 3x 2 1
9 K 3x
3Kx
2x R 12
xR6
26. G raph each inequality.
1
2
3
4
5
6
7
1
2
3
27. G raph the solution set. T hen w rite the solution as a com pound inequality.
1
Chapter 1
2
3
4
5
6
7
23 K x R 6
20
4
5
6
7
Copyright © by Pearson Education, Inc. or its affiliates. All Rights Reserved.
24. D escribe the solution set ofthe inequality.
P ro b lem 6
So lv in g an Or In eq uality
G o t It? W hat is the solution of 7w 1 3 S 11 or 4w 2 1 R 213? G rap h the solution.
28. C ross out th e inequality that is N O T a solution to eith er 7w 1 3 . 11or 4w 2 1 , 213.
w . 1 71
w , 23
w.1
29. G raph th e solution.
5
4
3
2
0
1
1
2
3
4
5
30. T h e solution to 7w 1 3 . 11 or 4w 2 1 , 213 is all real numbers
less than 23 or greater than 1 17 .
Lesso n C heck • D o y o u U N D ER STA N D ?
Reasoning M ake up an exam p le to help exp lain why you m ust reverse the inequality
sym bol when you m ultip ly or divide by a negative num ber.
W rite T for true or F for false.
T
F
31. 5 . 24
T
32. (21)5 . (21)(24)
5
33. 21 , 24
21
Copyright © by Pearson Education, Inc. or its affiliates. All Rights Reserved.
34. E xplain w hat to do to multiply or divide an inequality by a negative number.
Exp lan atio n s m ay vary. Sam p le: In o rd er fo r th e in eq u ality still to b e
_______________________________________________________________________
tru e after m u ltip lyin g b o th sid es b y 21, I m u st reverse th e in eq u ality
_______________________________________________________________________
sym b o l.
_______________________________________________________________________
Math Success
Check off the vocabulary words that you understand.
compound inequality
“and” inequality
“or” inequality
R ate how well you can solve and graph inequalities.
N eed to
rev iew
0
2
4
6
8
N ow I
g et it!
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Lesso n 1-5