Download 1.2 - Variables, Expressions, and Equations

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1.2 - Variables, Expressions, and Equations
Algebra Vocabulary
Variables are letters that are used to represent numbers in algebra.
Coefficient is the number in front of a variable; This means "the number times the letter".
✪ NOTE: The coefficient includes the sign in front of the number also. ✪
Term is the combined form of the variable and its coeffiecient
Like Terms are terms that have the same variables and degree (power).
Expression is a number sentence. You simplify expressions. You can not solve an expression.
Variable Expression is an expression that has at least one variable in it.
EXAMPLE: Identifying Parts of an Algebraic Expression
Directions: Identify the variables, coefficients, constants, and like terms for the following:
1) 5x + 3 - 6x + 3x2 + 6y
2) 4 + 6
3) 4xy + 5x + 3y + 4x2
Solution:
1) Variables: x an y; Coefficients: 5, -6, 3, 6; Constants: 3; Like Terms: 5x and -6x
2) Variables: none; Coefficients: none; Constants: 4 and 6; Like Terms: 4 and 6
3) Variables: x an y; Coefficients: 4, 5, 3, 4; Constants: none; Like Terms: none
HOMEWORK EXAMPLE: Identify the variables, coefficients, constants, and like terms on #1 on Algebra Worksheet.
Variables Operations
Adding/Subtracting Variables - When you add variables make sure you have like terms.
To add variables:
1) Find all of one like term and add them together.
2) Find another kind of like term and add them together.
3) Anything that does not have any like terms just stays the same.
4) Rewrite the simplified expression with the highest degree first.
Common Mistakes when Adding Variables - DO NOT DO THE FOLLOWING!!!
Adding apples and oranges: x and x2 or x and y.
Forgetting about sign in front of coefficient: 6x + 2x - 3x, this should simplify to 5x.
Examples: Adding Variables
Directions: Simplify 5x + 3 + 6x + 3x2 + 2x
Solution:
A) Add the x's. 5x + 6x + 2x = 13x
B) There are no other like terms, so the "+ 3x2" and the "+ 3" just stay the same.
C) Rewrite the simplified expression: 3x2 + 13x + 3
HOMEWORK EXAMPLE: Simplify #36 on Algebra Worksheet.
Multiplying Variables - When you multiply variables, don't worry about like terms.
To multiply variables:
1) Multiply the numbers/coefficients.
2) Multiply the variables together; Raise the power if necessary.
3) Rewrite the simplified expression, putting the coefficient first then variable and letters in alphabetical order.
Common Mistakes when Adding Variables - DO NOT DO THE FOLLOWING!!!
Not raising the power: x · x = 2x ; should be x · x = x2.
Forgetting about sign in front of coefficient: 6x + 2x - 3x, this should simplify to 5x.
Examples: Multiplying Variables
Directions: Simplify 4 · 2x
Solution:
A) Multiply the numbers. 4 · 2 = 8
B) There are no variables to multiply.
C) Rewrite the simplified expression: 8x
Examples: Multiplying Variables
Directions: Simplify 4y · 2x
Solution:
A) Multiply the numbers. 4 · 2 = 8
B) Multiply Variables. y · x = xy
C) Rewrite the simplified expression: 8xy
Plugging into an Expression
Sometimes you know what number the variable is representing. You can "plug" the number into the expression for the variable. When
you do this you are evaluating the expression.
To evaluate expressions:
1) Plug in (with parentheses) for all of the known variables.
2) Perform the indicated operations.
3) Simplify as far as possible. Should be able to get down to one number.
Examples: Evaluate the for 5x + 3 when x = 3.
Solution:
A) Plug in for the x's. 5(3) + 3
B) Perform the indicated operations: 5(3) = 15
C) Simplify as far as possible. 15 + 3 = 18
HOMEWORK EXAMPLE: Exercise 15 on page 16.
edHelper.com - Beginning Algebra
08/22/2007 09:26 AM
Name _____________________________
Date ___________________
Algebra
(Answer ID # 0573083)
Combine like terms.
1. 9z 2 + 19z 2 + 13z + 11z + 18 - 2 + 3
2. 10 - 5k + 8k + 17 - 7
3. 12b2 + 14b - 16
4. g + 15 - 4g - 6g
5. 6a + 7a - 18a 2 + 13a 2 - 2a 3 + 8a 4
6. 3m - 17m - 1 - 16 - 15m
7. 19h2 - 10h - 12h - 11 - 4h2 - 5
8. 14y + 9y2 - 2 + y
9. 6f + 14f + 11f 2 + 17f 3 - 19f + 9f + 13f 4
10. 7d - 18d
11. 8w2 - 5w3 - 15w2 + 16w - 3w3 - 10w
12. 12v + 4 - 2 + 8 + 3
13. 7r 2 - 9r 2 + 5
14. 17h + h + 16 - 6h
15. 14r - 4 + 12
16. 15s - 18s 2 + 19s - 11s 4 - 13s - 10s
17. 15 + 17f 2 - 5f 2 - 16f 2
18. 4n + 2n - 11n - 13n + 18n
19. 6z - 10 + 12z 2 + 14z + 8 + 9z 2 - 3z
20. 7 + 1 + 19 + 19c - 11c
21. 16d2 + 9d2 - 12d4 - 8d3
22. 10 - 15v - 17v2 + 7 + 13v2 - 4 + 18v
23. p + 6 + 2p2 - 14p2 + 5 - 3p
24. 19 + 5e - 15
25. 4g + 16 + 12g - 3 + 8
26. x + 18x2 + 10 + 7x2 + 9 + 13x - 14x2
27. 17q + 6 - 11q2 - 15q
28. 2w2 - 19w2 + 5w - 7w + 11w4 + 4w
29. 17 - 3m - 16m
30. 9a + 14 - 2a - 13
31. 1 - 15 + 10j + 18j 2 + 12 - 8j 2 + 6j
32. 8y + 10y4 - 4y3 - 15y2 - 2y
33. 3t + 17t
34. 9u + 13u2 - 19 + 14 + 11u2 - 12u
35. 5b - 18b + 16 - b + 7
36. 6k2 + 15k - 8 + 9k2
37. 17t + 5t
38. a - 12a 2 + 11a - 4a + 13a 2 + 6a 4
39. 16y2 - 19y + 14 - 10
40. 18e + 2 - 3e + 7 + 11
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