1. 6.1 Algebraic Expressions & Formulas
Practice:
PG 314: 1, 3, 5, 11, 27, 31, 33, 39
PG 315: 41, 43, 47, 49, 53, 59, 67
PG 329: 3, 13, 19

2. What have we seen so far? What we will be looking at: 3+𝑥=5 3∙𝑥=6
3÷𝑥= 3 2
3−𝑥=1
3+2=5
3×2=6
3÷2= 3 2
3−2=1
And much more!

3. Evaluating Algebraic Expressions
What is an algebraic expression?
A combination of variables and numbers using operations of addition, subtraction, multiplication, division, powers, and/or roots
Evaluating an algebraic expression means finding the value of the expression for a given value of the variable.
𝑥 𝑥− 𝑥 𝑥 𝑥 𝑥 𝑥 2

4. Example: Evaluating Algebraic Expressions
Use x = 2 when solving the following: 𝑥+6=2+6=8 5 𝑥 2 =5 2 2 =5 4 =20 Your turn! Try: 4𝑥+3=4 2 +3=8+3=11

5. Formulas and Mathematical Models
An equation is formed when an equal sign is placed between two algebraic expressions.
A formula is an equation that uses variables to express a relationship between two or more quantities.
The process of finding formulas to describe real-world phenomena is called mathematical modeling.

6. Vocabulary
Terms – the parts of an algebraic expression separated by addition
Coefficient – the numerical portion of a term
(IF you see a letter with no number in front of it, i.e. “y,” the coefficient is 1. There is always a coefficient!)
Constant – a term that consists of just a number
Factors – the parts of the term that are multiplied
Like terms – terms that have the same variable as factors
7𝑥−9𝑦+2𝑥−3
Term Term Term Term
Like terms

7. Vocabulary Continued 7𝑥−9𝑦+2𝑥−3
Terms are: 7x -9y 2x -3 Factors of the terms: 7, x -9, y 2, x -3 Coefficients: Constants: -3 Variables: x and y Like terms: 7x 2x
7𝑥−9𝑦+2𝑥−3

8. Identifying Parts of Algebraic Expressions
List the terms, like terms, factors, coefficients, and constants of the following expressions.
6𝑦−5𝑥−2+3𝑦+2 𝑥 2
Terms: 6y, -5x, -2, 3y, 2x2
Like terms: 6y and 3y
Factors: 6y: 6, y
-5x: -5, x
-2: -2
3y: 3, y
2x2: 2, x2
Coefficients: 6, -5, -2, 3, 2
Constants: -2
8𝑥−2−𝑦+7𝑦+3+3 𝑥 2
Terms: 8x, -2, -y, 7y, 3, 3x2
Like terms: -y and 7y, -2 and 3
Factors: 8x: 8, x
-2: -2
-y: -1, y
7y: 7, y
3: 3
3x2: 3, x2
Coefficients: 8, -2, -1, 7, 3, 3
Constants: -2, 3

9. Simplifying Algebraic Expressions
Properties that we will be using:
Commutative
Of Addition
Of Multiplication
Associative
Distributive
Combining like terms:
5𝑥+2𝑥=7𝑥 𝑥+7𝑦+2𝑥= 7x + 7y
The result of combining like terms is a simplified algebraic expression!

10. Examples of Simplifying Algebraic Expressions
6 2 𝑥 2 +4𝑥 𝑥 2 +3𝑥 =6∙2 𝑥 2 +6∙4𝑥+10∙4 𝑥 2 +10∙3𝑥 =12 𝑥 2 +24𝑥+40 𝑥 2 +30𝑥 =52 𝑥 2 +54𝑥 8𝑥+2 5− 𝑥−3 =8𝑥+2(5)−2 𝑥−3 =8𝑥+10−2𝑥+6 =6𝑥+16

11. 6.2 Linear Equations

12. What is a linear equation?
A linear equation is an equation that is in the form ax+b = c where a, b, and c are any value.
X is the variable that we are going to solve these equations for.

13. How do you solve linear equations?
Simplify the equations using the distribution property and combining like terms.
Use addition and subtraction properties to move x to one side of the equation.
Use multiplication and division properties to isolate x.
Check your answer by evaluating your original equation for x. Just plug in x and use the order of operations.

14. Practice 2x + 3 = 17 2𝑥+3−3=17−3 2𝑥=14 → 1 2 2𝑥= 1 2 14 → 𝑥=7
2𝑥= → 𝑥= → 𝑥=7
You try 3x – 6 = 9
3𝑥−6+6= → 𝑥= → 𝑥 3 = 15 3
𝑥=5

15. More Practice 3(x - 4) – 5x = -5 3𝑥−3 4 −5𝑥=−5 → 3𝑥−12−5𝑥=−5
3𝑥−3 4 −5𝑥=−5 → 𝑥−12−5𝑥=−5
−2𝑥−12=−5 → −2𝑥−12+12=−5+12
−2𝑥=7 → − 2𝑥 −2 = 7 − → 𝑥=− 7 2
You try
2(x + 6) + 3x = -2
2𝑥+12+3𝑥=− 𝑥+12=−2
5𝑥+12−12=−2− 𝑥=− 𝑥 5 =− 14 5
𝑥=− 14 5

16. Example 2
𝑥 4 = ∙ 𝑥 4 =4∙ 𝑥=12
Your Turn
𝑥 2 = ∙ 𝑥 2 =2∙ 𝑥=12