algebra ch. 6 review

pg. 449

12. x/x+1+1/2x+2=7/8

-7/8,x/x+1/2x+2

factor, simplify, combine like terms, find the lcd.

build the denominator to have the same number for the bottom.

8 is the lcd

8(x+1)(X 1
______+ __ = 8(x+1) 7/8


(X+1) 2(x+1)

8x+8x 8x+8
________+
x+1 _________ x

2

cancel out the x+1

4x(2-2)(2+2x)+ 8x+4=7x+7

7 multiply by x= 7x using the distributive method


8-1=7

answer 8x+4=7x+7

combine like terms;

x=3

Marie Zajac

Bachelor's Degree in psychology with a concentration in rehabilitation counseling.

intermediate algebra review of ch. 1-6 pg. 449

review ch. 1-6. pg 449

solve each equation:

1. 3x-2=5

3x-2+2=2+5

3x=7

x=7/3

the solution to the equation is 7/3.

2. 3/5x =-2

3/5x.5/3=-2.5/3

x=10/3

in a fraction a person can think of it as a division; multiply, invert, to both sides of the equation.

3. 2(x-2)=4x

this is a multiplication

2x-4=4x

2x-2x-4=4x-2

-4=2x factored and lcd with 2 in both -4 and 2.

2/-4=-2=2x/2

-2=x

4. 2(x-2)=2x

2x-4=2x
2x-2x-4=0

-4=0

5. 2(x+3)=6x+6

2x+6=6x+6

2x=6x

2x-2x=2x-6x

0=4x

0=x

6. 2(3x+4)+x2=0

6x+8+x2=0

combine like terms

x2+6x+8=0

factor out the terms

(x+2)(x+4)=0

muldtiply x2.8=8x2 4+2=6 4.2=8

X=-2 or x=-4.

x+2=0 x+4=0.

Marie Zajac BA in psychology with a concentration in rehabitation counseling.

6.1 pg. 381 ex.4 Reducing

Reducing:

a) 30/42 15/21
2/30
2/42
3/15=5
3/21=7
the problem has been factored out to the gcf;
the 2's and the 3's have been cancelled out
30/42 reduced to lowest terms=5/7.

b) x2-9/6x+18

factor and reduce by the same number find the gcf and cancel out like terms.

(x-3)(x+3)/6(X+3) factor out the x+3'S x-3/6

x2-9/6x+18 is reduced to lowest terms=x-3/6.

c) 3x2+9x+6/2x2-8

3(x+2)(x+1) look into the answer.

continuation of the previous blog

a) 30/42

15/21 2

5/7 3

2/2 3/3 5/7

reducing to lowest terms is to divide each numerator and the denominator by the same number; then cancel like numbers.

b) x2-9
_______


6x+18

first factor

(x+3)(x-3)
_____________
6(x+3)

cancel out the x+3
(x-3)/6

until next time

ch. 6 pg. 380 reducing to lowest terms

Reducing to lowest terms by mutipling the numerator and the denominator by the same number.

ex. 3/5 to 6/10
3.2=6
5.2=10

reducing rational expressions can be done the same way.

a rational expression is expressed in lowest terms when the fraction can not
be put into lower terms except by the number 1. 1 does not change the value.

reducing to lowest terms a rational expression is completed the same way as with putting fractions in to the lowest terms by dividing the numerator and the denominator by the same number; then cancelling out the like terms.

ex. ab/ac to b/c the a's are the same; causes the a's to be cancelled out.

Ex. 4 pg. 381.

Reducing:

reducing to lowest terms;

30/42 factor out like terms;

2.3.5=30
2.3.7=42

30.2=60
42.2=422

ch.6 ex. problems 21-28 pg. 386

Find the domain of each rational expression:

The domain in an algebraic expression is a set of numbers that can be put in the place of a variable. For rational expressions, the domain must exclude any real numbers that cause the denominator to be 0.

21. x2+X
_______=+2

x-2

all real numbers except 2.

23. x
________

x2+5x+6

all real numbers except -3 and -2.

use factorization with distributive and associative properties;

is 0 if; (x+2)(x+3)=0. or

x+2=0 OR x+3=0

The set of domain is the set of all real numbers except -3, and -2.

25. x2-4
________= R

2

The answer is R because the denominator is 2.

27. x-5
____= all real numbers except 0.

That is all for now.

Marie Zajac
Bachelor of Arts degree in Psychology

x

algebra ex.3 pg. 379

ex. 3,

Domain:

is the set of all real numbers that can be used in place of the variable.

The domain must exclude all of the numbers for which would cause the denominator to = to 0.

a) x2-9/x+3

with -3+3=0 determines that -3 can not be in the denominator.

the domain is the set of all real numbers that can be used in the place of a variable except -3. It is used in a set notation{x|xnot=-3}.

review the operations of adding and subtracting signed numbers.

b) x
____

x2 -x-6

1. figure out the domain and the number to exclude; then put it in a set notation.

2. the denominator needs to be factored.

x2 can be divided in to x2-x-6=0

(x-3)(x+2)=0 3.2=6 the 2 x's= x2 associative theory., distributive.

x-3=0 or x+2=0

x=3 or x= -2

review signs for multiplication;

review this problem again, as for as the - sign for the 3 and the -sign for the 2.

the set theory is as follows:

{x|xnot = to -2 and xnot=to 3} a negative 2 and a positive 3=0.

c). x-5
________
4

The denominator can not = to 0 since the d is 4. or -2, and 2=0

excercises from 21-28.

21. x2+x
_________
x-2

find the domain;

all real numbers except for +2.

23. -x
________

x2+5x+6

factor and use either associative or distributive.

(x+3)(x+2)

all real numbers except -3 -2.

25. x2-4
________
2

R because the denominator is 2

the denominator is the set of all real numbers.

27. x-5/x

all real numbers except 0.

that is all for now.

A Bacholor of Arts degree in Psychology will happen.
I am determined and have perserverance.

algebra ex.3 pg. 379

intermediate algebra ch 6. 6.1 ex.2

ex.2 Ruling out values for x:

1. the definition of a rational number includes the donominator not equaling to 0. ex. 5/0. or a /-8+8=0, if any combination of numbers=0 in the denominator then it is called undefined. In order for the equation to be considered a rational number the denominator can not =0.

2. ex. 2.

x2-4=0

use factorization:

(x-2)(x+2)=0

with the use of factorization; x-2=0, x+2=0; -2, 0R + 2=0

-2, or +2 can not be used in the denominator.

will be continued later.

intermediate algebra ch 6. 6.1

evaluating rational expressions:

a) find the value of;

4x-1/x+2 for x=-3

4.-3-1/-3+2= -12-1/-3+2= -13/-1=13

b) find the value of;

if R(x)=3x+2/2x-1, find R(4)

3.4+2/2.4-1=12+2=14/7=2

exercises 7-12

7. evaluate; 3x-3/x+5 for x=-2

3.-2-3/-2+5= -9/3=-3

8. evaluate; 3x+1/4x-4 for x=5

3.5+1/4.5-4=15+1/20-4=16/16=1

9. evaluate; if R(x)=2x+9/x find R(3)

2.3+9/3= 15/3=5

10. if R(x)=-20x-2/x-8 find R(-1)

-20.-1-2=-20+2=-18/-1-8=-9 18/9=2

11. if R(x)=X-5/X-3 find r(2),R(-3.02), and R(-2.96).

algebra ch. 6

Order of operation:

1. simplify all numbers within the (), { }, [].

2. work the enclosed numbers within the (), etc., the innermost then work outward.

3. work separetly above and below any fraction bars

simplyfy any exponets and roots.

4. do any mutipication and devision working from left to right.

5. do any addition and subtraction.

evaluate:

3x-3
________ x=-2

x+5



3.-2 / -2+5 -6/3= -3.

That ia all for now.

soon to have a bachelor's degree.




x+5



______

intermediate algebra ch 6.

Ch. 6 page: 377

Rational expressions:

is the ratio of two integers with a demonator not 0.

a rational number is reduced to lowest terms by dividing the numerator and
demoninator by the gcf.

for example:

3/4 -9/-6, -7/1, and 0/2 are rational numbers.

an example of a rational expression:

x2 - 1
_______

x + 8, 3/7, 9x, 3a2+ 5a-3
___________________

a-9

math 115 least common mutiple and more as a review

The difintion of the least common multiple:

is the smallest natural number that is a multiple of the 2 groups.

The lcm of 240 and 450.

10 is a mutiple of both numbers

5 is a mutiple

2 is a mutiple.

2 is the lcm of 240 and 450.

perform the operation:

(-18+6)-(10+20)/14-8

use the order of operations method:
2 neg. = a +
work inside the () first then mutiply or divide.

18-6=12- 30/14-8
the 18 had the bigger number; the sign goes with the larger number.
-12-30= two negatives= a + sign. = a -42. 30+12=-42.
14-18=4
42/4=21/2 as a fraction is the lowest terms.

that is all for now.

Marie Zajac
soon to have a bachelor's degree in psychology.