This document provides an introduction to algebra concepts including expressions, equations, inequalities, and order of operations. It uses word problems to demonstrate how algebra can be used to solve for unknown values. Step-by-step examples are provided to show algebraic operations like combining like terms, distributing, and substituting values. Key terms are defined to build a foundation for algebraic thinking and problem solving.

1. Algebra
Lesson 5
Tennessee
Adult Education
This curriculum was written with funding of the Tennessee Department of Labor and Workforce Development and may not be reproduced in any way without written permission. ©

2. What is Algebra?
A clown was carrying a handful of balloons.
Along came the wind and blew 8 away, leaving
him only with 9. How many did he start with?
Algebra takes real life problems and puts
them into math so we can solve them.
x-8 = 9
The goal in Algebra is to find out the
unknown!

3. A scale has 20 pennies on one side . On the other side is 6 pennies
and an unknown amount of pennies. Both sides equal the same
weight.
20 = 6 + x
20 6 pennies
pennies + ? pennies

4. x-8 = 9
+8 +8
x = 17
x-8 9

5. What is Algebra?
A clown had 17 balloons. Along came the wind
and blew 8 away, leaving him only with 9.
The goal in Algebra is
to find out the
unknown!

6. -Different signs subtract numbers
-Always keep the sign of the larger number
when subtracting and adding
-3 + 7 = 4
- - - +++ +++ +

7. -2 + 9 = 7
- - +++ +++ +++

8. -4 + 2 = -2
- - - - ++

9. -7 + 5 = -2
- - - - - - - +++ ++

10. -3 + 16 = 13
--- +++ +
+++ +++ +++ +++

11. -if both negatives, add together
- keep the negative sign
-5 + -5 = -10
--- --
--- --

12. -8 + -4 = -12
--- --- --
--- -

13. In math 2 negatives (-)(-)
equal a positive (+)

14. -4 – (-3) =
-4 + 3 = -1
--- -
+++

15. -8 – (-4) =
-8 + 4 = -4
--- --- --
+++ +

16. -6 – (-8) =
-6 + 8 = 2
--- ---
+++ +++ ++

17. -2 – (-7) =
-2 + 7 = 5
--
+++ +++ +

18. -9 – (-3) =
-9 + 3 = -6
--- --- ---
+++ +++

19. Rule Add/Subtract
Same signs - 1+3= 4
add numbers
-1 - 3 = -4
Different signs - -3 + 4 = 1
subtract numbers
4–3=1
Keep sign of the largest number
Rule Add/Subtract
++ 4 + (-2) =
-- 4–2=2
+- -3 – (-4) =
-+ -3 + 4 = 1

20. Guided Practice
1. +8 – 14 = ______ 7. 5 x -3 = ______
2. -2 + 11 = ______ 8. -6 x 2 = ______
3. -33 - 22 = ______ 9. -4 x -8 = ______
4. (-7) + (-3) = ______ 10. 42 ÷ -7= ______
5. (-10) + (16) = ______ 11. -3 x -9 = ______
6. -4 – (-4) = ______ 12. -20 ÷-2 = ______

21. Order of Operations
Please Excuse My Dear Aunt Sally
1. Parenthesis (4-2)
2. Exponent 4³
3. Multiply 4(3) or 4x3
4. Divide 4÷2 or 4/2
5. Add 4+2
6. Subtract 4-2

22. (6-4)² - 2 =
(2) ²- 2 =
4–2=
2

23. (6x2)(8÷2) ² =
(12)(4) ² =
(12)(16) =
192

24. 2(3 + 2 x 6 -1)² =
2(3 + 12 – 1) ² =
2(15 – 1) ² =
2(14) ² =
2(196) =
392

25. 3x4+6÷2+5-1
12 + 6 ÷ 2 + 5 – 1
12 + 3 + 5 – 1
15 + 5 – 1
20 – 1
19

26. Key Terms
• product multiply
• squared times itself
• sum add
• difference subtract
• half divide by 2 or ½
• quotient divide
• decreased subtract

27. Guided Practice
six more than the square of four is twenty two=
4² + 6 = 22
5x – 1 = 7
one less than five times a number equals seven
the quotient of a twelve and four plus a number
12 ÷ 4 + n

28. Algebra Rules
1. What you do to one side you must do to the other. This keeps
them equal.
2. You must get the variable by itself to find out what number
value it equals.

29. Guided Practice
-4 = x + 2 ½ n -4 = 9-2
-2 -2 ½ n -4 = 7
x = -6 +4 +4
½ n = 11
3 + 2n = 43 2( ½ n) = 11(2)
-3 -3 n = 22
2n = 40
2 2
n = 20

30. Substitution
– you put the number where the letter was
what is:
x-2
if x = 6
6 -2 = 4

31. Guided Practice
3(n) – 2(4) + 16 / x if x = 4
3(4) – 2(4) + 16 / 4
12 – 8 + 16 / 4
12 – 8 + 4
12 – 12
0

32. Guided Practice
b³c + bc + 2b² if b = 3; c = 4
(3) ³(4) + (3)(4) + 2(3) ²
9(4) + (3)(4) + 2(9)
36 + 12 + 18
66

33. Key Terms
• expression
– a way to represent spoken information about an
unknown number:
“a number plus 3” = n + 3
• equation
– shows that two quantities are equal
• inequality
– uses symbols < and > to show “greater than” and
“less than”