The Algebra Tutor

Lesson #1
Addition Property of Equality

This lesson introduces the principle of the addition property of equality. Mastering this concept will enable the student to solve basic algebraic equations and simple word problems in the form of x + a = b where a and b are numbers. Areas discussed include: equations, true and false statements, open sentences and basic equations with examples and practice of each type of problem. Word problems and general set up are discussed with accompanying examples and practice problems.

PRACTICE PROBLEMS AND ANSWERS
1. b ­ 15 = ­32

2. ­12 + z = ­36

3. ­27 ­ x = ­ 7

4. y ­ (­ 1.3 ) = ­ 7.1

5. k + (­ 3/5 ) = 5/3

6. j + 16 = ­ 4

7. x + 13 = 5

8. Some number added to ­ 16 is equal to 39. What is the number?

9. The temperature at dawn was ­2 degrees. At one the temperature was 15 degrees. What was the change in temperature?

10. Richard's golf score was 68. This was 4 less than Cindy's golf score. What was Cindy's score?

11. When 9 is subtracted from another integer, the difference is ­ 13. What is the other integer?

12. x ­ 2/3 = ­ 5/6

13. A number decreased by 11 is 40. Find the number.

14. n ­ 1/2 = 2/5

15. ­20 = x ­ ( ­14 )

Answers:
1. (b = ­17),  2. (z = ­24),  3. (x = ­ 20)
4. (y = ­ 8.4),  5. ( k = 34/15),  6. (j = -20)
7. (x = ­8),  8. (55),  9. (It went up 17 degrees.)
10. (72),  11. (The other integer is ­4),  12. ( x = ­ 1/6)
13. (the number is 51),  14. ( n = 9/10),  15. ( x = ­ 34)


STUDENT VOCABULARY
Variable: A term used in a mathematical equation to represent an unknown number.

Addition Property of Equality: A mathematical property that allows a number or term to be added to both sides of an equation and still maintain the equality.

Open Sentence: A sentence containing a variable. The variable has not yet been assigned a value or the equation has not been solved. e.g. x + 9 = 10

Equation: A mathematical sentence that contains the equal sign.
e.g. 3 + x = 5, 2 + 4 = 6.

Positive Number: A number greater than zero.

Negative Number: A number less than zero.

Additive Inverse: A number and its additive inverse always add to 0. e.g. (­3) + (3) = 0, x + (­x) = 0.

False Statement: An equation which has been solved for the variable, but the solution is incorrect. When the value selected for the variable is placed in the original statement, the answer will not be correct. e.g. 2x ­ 6 = 10, x = 5.
check: 2(5) ­ 6 = 10 , 4 = 10 therefore a false statement.

True Statement: An equation which has been solved for the variable, and the solution is correct. Correct solutions when replaced in the original equation will result in both sides being equal to the same quantity e.g. 3x ­ 6 = 6, x = 4.
check: 3(4) ­ 6 = 6, 12 ­ 6 = 6 therefore a true statement.

Denominator: The bottom portion of a fraction e.g. in the fraction 3/4, 4 is the denominator of the fraction.

Numerator: The top portion of a fraction. e.g. in the fraction 3/4, 3 is the numerator of the fraction.

Integer: A whole number that can be positive or negative.


QUESTIONS FOR THOUGHT AND FURTHER STUDY
1. Match the equation with the correct definition:
    a. true     A. (x + 3 = 8)
    b. false        B. (2 + 2 = 4)
    c. open     C. (2 + 3 = 10)

2. Explain the addition property of equality.

3. Explain what makes a statement true, false, or neither.

4. What are the seven steps that should be used in to order to set­up and solve a word problem?

5. What is the only number that may not be used in the denominator of a fraction?

6. What four words frequently used in word problems indicate the operation of addition?

7. What symbol used in word problems to represent the word "is"?

8. What words frequently used in word problems indicate subtraction?

Answers:
1. a. B. , b. C. , c. A

2. (A mathematical property that allows a number to be added to both sides of an equation and still maintain the equality.)

3. (If the final solution of an equation results in both sides being equal then it is true. If the final solution of an equation results in each side with a different answer, then it is false. If the equation is not solved then it is open.)

4. (See video for answer)

5. (Zero)

6. (Sum, added to, total, plus).

7. (The equal sign =)

8. (Less, decreased, minus).


COLLECT THE WHOLE SERIES
Volume 1
The Addition Property of Equality

Volume 2
The Multiplication Property of Equality

Volume 3
The Addition & Multiplication Property of Equality

Volume 4
Removing Grouping Symbols

Volume 5
Exponents & Properties of Exponents