INSTRUCTOR RESOURCE SOLUTION MANUAL College Algebra Graphs and Models Bittinger 7th edition - SOLUTION MANUAL

,SOLUTION MANUAL College Algebra Graphs and
Models, 7th edition Bittinger
Notes
1- The file is chapter after chapter.
2- We have shown you few pages sample.
3- The file contains all Appendix and Excel sheet
if it exists.
4- We have all what you need, we make update
at every time. There are many new editions
waiting you.
5- If you think you purchased the wrong file You
can contact us at every time, we can replace it
with true one.
Our email:


,Just-in-Time Review
√ √ √ √
4. 6 = 6, so it is true that 6 ≤ 6.
1. Real Numbers
5. −30 is to the left of −25 on the number line, so it i
that −30 > −25.
2 √ 8 4 16 5 25 16
1. Rational numbers: , 6, −2.45, 18.4, −11, 3 27, − , 6. − =− and − = − ; − is to the right of
√ 3 7 5 20 4 20 20
0, 16 4 5
so it is true that − > − .
2 8 5 4
2. Rational numbers but not integers: , −2.45, 18.4, −
3 7
√ √ √ √
3. Irrational numbers: 3, 6 26, 7.151551555 . . . , − 35, 5 3 4. Absolute Value
(Although there is a pattern in 7.151551555 . . . , there is
no repeating block of digits.)
√ √ 1. | − 98| = 98 (|a| = −a, if a < 0.)
4. Integers: 6, −11, 3 27, 0, 16
2. |0| = 0 (|a| = a, if a ≥ 0.)
√ √
5. Whole numbers: 6, 3 27, 0, 16
3. |4.7| = 4.7 (|a| = a, if a ≥ 0.)
6. Real numbers: All of them  
 2 2

4.  −  = (|a| = −a, if a < 0.)
3 3
2. Properties of Real Numbers 5. | − 7 − 13| = | − 20| = 20, or
|13 − (−7)| = |13 + 7| = |20| = 20
1. −24 + 24 = 0 illustrates the additive inverse property. 6. |2 − 14.6| = | − 12.6| = 12.6, or
2. 7(xy) = (7x)y illustrates the associative property of mul- |14.6 − 2| = |12.6| = 12.6
tiplication.
7. | − 39 − (−28)| = | − 39 + 28| = | − 11| = 11, or
3. 9(r − s) = 9r − 9s illustrates a distributive property. | − 28 − (−39)| = | − 28 + 39| = |11| = 11
     
4. 11 + z = z + 11 illustrates the commutative property of  3 15   6 15   21  21
addition. 8.  − −  =  − −  =  −  = , or
4 8 8 8 8 8
      
5. −20 · 1 = −20 illustrates the multiplicative identity prop-  15     
 − − 3  =  15 + 6  =  21  = 21
erty. 8 4   8 8  8  8
6. 5(x + y) = (x + y)5 illustrates the commutative property
of multiplication.
5. Operations Using Fraction Notation
7. q + 0 = q illustrates the additive identity property.
1 1 3 1 4 3 5 4 15 4 + 15 19
8. 75 · = 1 illustrates the multiplicative inverse property. 1. + = · + · = + = =
75 5 4 5 4 4 5 20 20 20 20
9. (x+y)+w = x+(y+w) illustrates the associative property 3 1 3 1 5 3 5 8 4·2 4
2. + = + · = + = = =
of addition. 10 2 10 2 5 10 10 10 5·2 5
10. 8(a + b) = 8a + 8b illustrates a distributive property. 3 5 3 3 5 4 9 20 29
3. + = · + · = + =
8 6 8 3 6 4 24 24 24
5 5 9 5 27 32
4. +3= +3· = + =
3. Order on the Number Line 9 9 9 9 9 9
7 3 7 3 2 7 6 1
5. − = − · = − =
1. 9 is to the right of −9 on the number line, so it is false 8 4 8 4 2 8 8 8
that 9 < −9. 10 2 10 3 2 11 30 22 8
6. − = · − · = − =
2. −10 is to the left of −1 on the number line, so it is true 11 3 11 3 3 11 33 33 33
that −10 ≤ −1. 3 7 3 14 3 11
7. 2 − =2· − = − =
√ √ √ 7 7 7 7 7 7
3. −5 = − 25, and − 26 is to the left of√− 25, or −5, on
the number line. Thus it is true that − 26 < −5. 5 3 5·3 15 5·3 3
8. · = = = =
8 10 8 · 10 80 5 · 16 16

Copyright 
c 2025 Pearson Education, Inc.

, 2 Just-in-Time R

3 5 3·5 15 18. First we write each mixed numeral as a fraction.
9. · = =
4 8 4·8 32 1 1 5 1 5 1 6
1 =1+ =1· + = + =
5 2 5 3 15 3·5 5 5 5 5 5 5 5 5
10. ÷ = · = = = 1 1 4 1 8 1 9
6 3 6 2 12 3·4 4 2 =2+ =2· + = + =
4 4 4 4 4 4 4
3 4 48
11. 12 ÷ = 12 · = = 16 Then we divide.
4 3 3 6 9 6 4 24 8·3 8
÷ = · = = =
5 5 4 5 9 45 15 · 3 15
5 3 5 4 20 10 · 2 10
12. 6 = ÷ = · = = =
3 6 4 6 3 18 9·2 9
4 6. Operations with Real Numbers
1 1 6 1 30 1 31
13. 5 =5+ =5· + = + =
6 6 6 6 6 6 6 1. 8 − (−11) = 8 + 11 = 19
14. We divide.  
3 1 3·1 3 1 1 1
2. − · − = = · =1· =
 3 10 3 10 · 3 3 10 10 10
9 32 32 5
=3 3. 15 ÷ (−3) = −5
−27 9 9
5 4. −4 − (−1) = −4 + 1 = −3

1 5. 7 · (−50) = −350
15. First we write 4as a fraction.
2 6. −0.5 − 5 = −0.5 + (−5) = −5.5
1 1 2 1 8 1 9
4 =4+ =4· + = + = 7. −3 + 27 = 24
2 2 2 2 2 2 2
Then we add. 8. −400 ÷ −40 = 10
1 2 9 2 9 3 2 2 27 4 31 9. 4.2 · (−3) = −12.6
4 + = + = · + · = + =
2 3 2 3 2 3 3 2 6 6 6
10. −13 − (−33) = −13 + 33 = 20
31
Finally we divide to write as a mixed numeral.
6 11. −60 + 45 = −15
   
 5 1 2 1 2 3 4 1
6 31 12. − = + − = + − =−
31 1 2 3 2 3 6 6 6
=5
−30 6 6 13. −24 ÷ 3 = −8
1
14. −6 + (−16) = −22
16. First we write each mixed numeral as a fraction.    
1 5 1 8 1·8 1·2/·4
5 5 9 5 18 5 23 15. − ÷ − =− · − = = =
2 =2+ =2· + = + = 2 8 2 5 2·5 2·5
/
9 9 9 9 9 9 9
1 1 3 1 3 1 4
1 =1+ =1· + = + = 7. Interval Notation
3 3 3 3 3 3 3
Then we subtract.
1. This is a closed interval, so we use brackets. Interv
23 4 23 4 3 23 12 11 tation is [−5, 5].
− = − · = − =
9 3 9 3 3 9 9 9
2. This is a half-open interval. We use a parenthe
11
Finally we divide to write as a mixed numeral. the left and a bracket on the right. Interval nota
9 (−3, −1].
 1
9 11 3. This interval is of unlimited extent in the negative
11 2
=1 tion, and the endpoint −2 is included. Interval nota
−9 9 9 (−∞, −2].
2
4. This interval is of unlimited extent in the positive
1 tion, and the endpoint 3.8 is not included. Interval
17. First we write 3 as a fraction.
3 tion is (3.8, ∞).
1 1 3 1 9 1 10
3 =3+ =3· + = + = 5. {x|7 < x}, or {x|x > 7}.
3 3 3 3 3 3 3
Then we multiply and simplify. This interval is of unlimited extent in the positive dir
1 9 10 9 90 and the endpoint 7 is not included. Interval nota
3 · = · = =3 (7, ∞).
3 10 3 10 30


Copyright 
c 2025 Pearson Education, Inc.