1. Variables

2. Variables Vary
x =
5.5
5.5
4.5
0.02
0.01
2.5
1.3
1.4
1.5
3.33
3.5 –1
–3.7
–4.8
–5.9
–6.0
–2.6
–1.5 –2 –3 –4 –5
1.2
1.0 10 15 20 25 10 9 5 7 6 8 30 40
2,000
3,000
4,000
5,000
1,000
300 50
100
200
1.1

3. Algebraic Expressions
An Algebraic Expression is an expression that contains at least one Variable. x 4
x + 14
3x + 1
9 – x
Means
3 × x
Means
x ÷ 4

4. x = 8 (8) (8) (8) (8) 4 x x 3 + 1 x 9 – x =22 =25 =2 =1 + 14
Using Variables
x = 8
(8)
(8)
(8)
(8)
One way to use variables is to substitute their numerical value into an algebraic expression. 4 x x
+ 14 x
9 – x
=22
=25 =2 =1

5. x = 8 4 x x 3 + 1 x 9 – x =22 =25 =1 =2 + 14 Using Variables
One way to use variables is to substitute their numerical value into an algebraic expression 4 x x
+ 14 x
9 – x
=22
=25 =1 =2

6. x – 3 x + x x ÷ 2 x = 4 = 1 = 8 5x = 20 = 2 2x – 3 2(x + 5) = 5 = 18
Let’s Practice
x – 3
x = 4
x + x
= 1
= 8 5x
x ÷ 2
= 20
= 2
Means
5 × x
2x – 3
2(x + 5)
= 5
= 18
9x + 3
(x +10)×(x – 2)
= 39
= 28
10 – 2x
3x + 4x – 2
= 2
= 26

7. x – 3 x + x x ÷ 2 x = 4 = 1 = 8 5x = 20 = 2 2x – 3 2(x + 5) = 5 = 18
Let’s Practice
x – 3
x = 4
x + x
= 1
= 8 5x
x ÷ 2
= 20
= 2
2x – 3
2(x + 5)
= 5
= 18
9x + 3
(x +10)×(x – 2)
= 39
= 28
10 – 2x
3x + 4x – 2
= 2
= 26

8. Let’s Practice with Two Variables
= 6
a = 3
b = 5
5a–b
= 10
2b – 3a
a(b + 5)
= 1
= 30
5a ÷ b
= 3
(a +10)×(b – 2)
= 39 ab
= 15
3ab + 4a – 2
= 55
Means
a × b

9. Let’s Practice with Two Variables
= 6
a = 3
b = 5
5a–b
= 10
2b – 3a
a(b + 5)
= 1
= 30
5a ÷ b
= 3
(a +10)×(b – 2)
= 39 ab
= 15
3ab + 4a – 2
= 55

10. 5 + x = 8 An Equation Unknown Unknown Variables
Another way to use a variable is as an unknown value in an algebraic equation.
Left
Side
Right
Side
5 + x = 8
An Equation
Claims that the Left Side = the Right Side
Unknown

11. 5 + x = 8 An Equation Unknown Variables = ≠ If: Left Side Right Side,
then the “equation is ”
true
If: Left Side Right Side, ≠
then the “equation is ”
false
To find the unknown value that makes the equation true, we “solve the equation for x.”

12. x 5 + = 8 12 8 = 8 True? If x = 7 , the equation is 7 False? True?
Unknown Variables
= 8 x 12 8
= 8
If x = 7 , the equation is
True? 7
False?
If x = 3 , the equation is
True? 3
False?

13. What value for x will make this equation true?
Solving an Equation
Solving an equation means finding a value for the unknown that makes the equation true.
5 + x = 3 8
What value for x will make this equation true?
So…….,
x = 3
is a solution to the equation.

14. Let’s Practice Using Different Variables
x – 3 = 10
x = 13
5a = 20
a = 4
4w – 3 = 5
w = 2
2δ ÷ 3 = 6
δ = 9
20 – □ = 2
□ = 18

15. Let’s Practice Using Different Variables
x – 3 = 10
x = 13
5a = 20
a = 4
4w – 3 = 5
w = 2
2δ ÷ 3 = 6
δ = 9
20 – □ = 2
□ = 18

16. Variables: Summary and Review
Substitute the numerical value of a variable into an algebraic expression 1
x = 4
x – 3 = 4 1 2
“Solve the equation for x.”
x + 17 = 25
x = 8 8

17. 5y + 6 coefficient variable constant Term Term Algebraic Expression