Answers to Basic Algebra Review
1. -1.1
Follow the sign rules when adding and subtracting:
If the numbers have the same sign, add them together and keep the sign.
If the numbers have different signs, subtract the numbers and keep the sign of the larger number.
2. 9
Follow the Order of Operations at all times. You can remember the Order of
Operations by the phrase “Please Excuse My Deal Aunt Sally”. For a more detailed explanation visit http://media.tripod.lycos.com/1782282/1373792.pdf
Parentheses Exponents
Multiplication / Division – starting at the left and moving to the right Addition
Subtraction
3. 41
Order of Operations was used to evaluate the expression.
2 2
2 2
3(1 5)
8
2
3( 4)
8
2
3(15) 8
4
45 8
4
49 8
41
Do what is inside parentheses first and rewrite the problem. Next do the exponents and rewrite the
problem. Next is multiplication, followed by addition and subtraction.
For more examples, visit
http://sradai.tripod.com/webonmediacontents/Order%20 of%20Operations%20Examples.pdf
4.
11
6
Follow the Order of Operations
2
2
3 5
3 25
22
22
11
6
2 3
6
2 9
6 18
12
6
5.
6
3 10
The problem states to “translate” the statement. It does not say to simplify. If it asked you to simplify, you would get 9 < 10.
6. >
As negative numbers become larger, they are getting smaller.
7. -36
Follow the sign rules for multiplying signed numbers. For more information, visit
http://sradai.tripod.com/webonmediacontents/Basic%20Rules%20to%20Remember. pdf
2 2
2
xy
2( 2)(3)
2( 2)(9)
4(9)
36
8.
3
x
4
3(
5) 11
3
15 11
3
4
x
x
x
9.
x
13
To get x by itself, add the opposite of -11 to both sides.
10.
x
7
4
7
21
4
28
7
x
x
x
11.
h
V
2r
These problems can be tricky. Since we want to get h by itself, we have to get everything away from it. We would need to divide both sides by
r
2 to get the halone.
12.
8
3
x
First we add the opposite of -5 to both sides to get the fraction and x by itself. Then multiply both sides by the reciprocal of the fraction.
3
5
7
4
3
2
4
4
3
2 4
3
4
1
3
8
3
x
x
x
x
13.
x
3
3(
6)
5
12
2
3
18
5
12
2
3
18
7
12
30 10
3
x
x
x
x
x
x
x
x
x
x
14.
x
4
0.3(
4)
0.5(3
)
0.7
1.2 1.5 0.5
1.2
0.3
4
x
x
x
x
x
x
x
15.
x
$70
Original price – 30% discount of original price = sale price x - 0.30x = 49
0.30
49
0.70
49
70
x
x
x
x
16.
x
18
Joe = x Jane = 3x + 8Equation:
3
8
80
4
8
80
4
72
18
x
x
x
x
x
To learn more about solving linear equations, visit
http://media.tripod.lycos.com/1782 282/1668263.pdf
To learn more about solving linear equations, visit
http://media.tripod.lycos.com/1782 282/1668263.pdf
17.
x
1
7
15 18
26
11 11
1
or
1
x
x
x
x
x
For the number line you would have a “closed circle” about the 1 and an arrow pointing to the left.
18.
x=-3
-8 -6 -4 -2 2 4 6 8
-5 5
x y
19.
y=-5x+1
-8 -6 -4 -2 2 4 6 8
-5 5
x y
20.
y=.25x+2
-8 -6 -4 -2 2 4 6 8
-5 5
x y
21.
1
12
2 1
2 1
8 9
1
1
11 ( 1)
11 1
12
y
y
Slope
m
x
x
22. Perpendicular
Compare the slope of each line. One is
2
3
and the other is3
2
which is thereciprocal and opposite sign of the first one. If I multiply these two slopes together, I would get -1 which indicates that it is perpendicular.
23.
y
3
x
3
Use the point-slope formula to find the equation of the line.
1
(
1)
( 9)
3(
4)
9
3
12
3
3
y
y
m x
x
y
x
y
x
y
x
24. -5
Substitute -2 in for x and evaluate.
2
3( 2)
7
3(4)
7
12
7
5
25.
128
7
( 2)
means to multiply -2 by itself 7 times. Since the exponent is odd, the answer will remain negative.26.
1
4x
2 6
2
6 4
1
x
x
x
x
x
27.
2
6
3
y
x
Follow the exponent rules.
28.
18
9
8
x
y
Apply the outside exponent to all exponents (and the invisible 1’s) first:
3 3 6
21 3
2
x y
x
y
Now change all negative exponents to positive exponents by following the rules and simplify.
21 18
3 6 3 9
8
8
x
x
x y y
y
29.
16
x y
6 3
22
x y
5 2
8
x y
4Distribute and follow the exponent rules for multiplying.
To learn more about negative exponents, visit
http://sradai.tripod.com/webonmediacontents/Negati ve%20Exponents.pdf
30.
3
x
2
5
x
9
Simplify following rules for like terms.
31.
6
x
2
11
x
8
When a minus sign appears outside parentheses, you will change the sign to positive AND change the sign of everything in the following parentheses to its opposite sign and then combine like terms.
32.
15
x
2
22
x
9
Use FOIL to multiply the two binomials together and then combine like terms.
33.
6
y
3
x
1
Since you are dividing a polynomial by a monomial, break up the problem into separate fractions with the same denominator and reduce.
34.
5
ab
2Look for the largest number each term has in common and the lowest exponent on the variables.
35.
6
xy
3(3
x
2
6
xy
2
2 )
y
Factoring guidelines can be found at
http://sradai.tripod.com/webonmediacontents/Factoring%20Part%201.pdf http://sradai.tripod.com/webonmediacontents/Factoring%20Part%202.pdf http://sradai.tripod.com/webonmediacontents/Factoring%20Part%202.pdf
Factoring is used extensively in algebra.
36.
(
x
9)(
x
9)
This is a difference of squares. Follow the factoring guidelines.
37.
(
x
9)(
x
3)
Follow the factoring guidelines.
38.
(2
x
5)(2
x
5)
This is a perfect square trinomial. Follow the factoring guidelines.
39.
(3
x
2)(
x
7)
Follow the factoring guidelines for using the ac method.
40.
2(
x
5)(
x
5)
First factor out the greatest common factor and then follow the guidelines for factoring the difference of squares.
41.
x
2 and 13
Factor the equation first and use the zero factor theorem to find the values for x. A quadratic equation will have two answers.
42.
x
4
43.
x
5
To find what makes a rational expression undefined, we set the denominator equal to zero and solve for the variable. An expression that is undefined means we are dividing by 0.
44.
3
2
x
First factor both the numerator and the denominator and then reduce like terms.
2
3
6
3(
2)
3
4
(
2)(
2)
(
2)
x
x
x
x
x
x
45.
5(
x
4)
Factor both of the rational expressions. Since we are dividing the rational
expressions, we need to remember “Keep, Change, Flip” when dividing fractions. Keep the first one, change division to multiplication, and flip the expression that comes after the division sign.
2
7
12
3
(
3)(
4)
3
5
5
25
5
5(
5)
Now rewrite the problem changing division to
multiplication and flipping the following fraction.
(
3)(
4) 5(
5)
5
3
Now cancel out the like terms.
5(
4)
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
46.
x
10Follow the rules for simplifying square roots found at:
47.
x
5Follow the rules for simplifying square roots.
48.
3
4
Follow the rules for simplifying square roots.
49.
8
x y
6 9Follow the rules for simplifying square roots.
50.
