1. Solving Linear Equations
Algebra I
Ms. Wiggins

2. Content Standards
HSA.CED.A.1 Create equations and inequalities in one variable and use them to solve problems.
HSA.REI.A.1 Explain each step in solving a simple equation as following from the quality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution.
HAS.REI.B.3
Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.

3. Do Now
Solve the equation x + 2 = 8 using all the vocabulary words (equivalent equations, inverse operations, isolate, solution of an equation and variable).

4. Objective
Students will be able to explain that each step in solving a linear equation follows from the equality in the previous step. Create and solve linear equations with one variable using the properties of equality.

5. Essential Understanding
Linear equations can be used to solve mathematical and real-world problems. You can solve linear equations by using the properties of equality.

6. Vocabulary Equivalent equations Inverse operations Isolate
Solution of an equation
Variable

7. Properties of Equality
Addition property
Subtraction property
Multiplication property
Division property

8. Use inverse operations
Use the opposite operation of what’s happening to isolate variables.
Example: x – 2 = 4
To solve this problems use the addition property since the subtraction property is being used. Add 2 to both sides.
X = 6
Example: x + 2 = 4
To solve this problems use the subtraction property since the addition property is being used. Subtract 2 from both sides.
X = 2

9. PEMDAS Don’t forget you still must apply PEMDAS when solving equations
Please (parenthesis)
Excuse (exponents)
My (multiplication)
Dear (division)
Aunt (addition)
Sally (subtraction)

10. Example 1: What’s the value of x in the equation 2(𝑥+4) 3 −8=32?

11. 2(𝑥+4) 3 −8=32 Students try: 4 + 3𝑥−1 2 = 9
Step 1: multiply each side by 3
(3) 2(𝑥+4) 3 −8(3)=32(3)
2(x + 4) – 24 = 96
Step 2: Distribute 2 into parenthesis and simplify.
2x -16 = 96
Step 3: inverse operation, add 16 to both sides of equation.
2x = 112
Step 4: inverse operation, divide 2 by both sides of equation.
X= 56

12. Example 2: The sum of three consecutive integers is 132
Example 2: The sum of three consecutive integers is 132. What are the three integers?
First integers = x; Second integer = x+1; Third integer = x+2
x + (x + 1) + (x + 2) = 132
Step 1: Combine like terms
3x + 3 = 132
Step 2: inverse operation, subtract three from both sides.
3x = 129
Step 3: inverse operation, divide three by both sides.
X = 43
The other two consecutive numbers after 43 is 44 & 45.

13. Example 3:
A lab technician needs 25 liters of a solution that is 15% acid for a certain experiment but she has only a solution that is 10% acid and a solution that is 30% acid. How many liters of the 10% and the 30% solutions should she mix to get what she needs?
Solution: Write an equation relating the number of liters of acid in each solution. Represent the total number of liters of one solution with a variable, like x. Then the total number of liters of the other solution must be 25 – x.

14. 25L of 15% solution = x L of 10% solution + (25-x) L of 30% solution
(.15)(25) = x (25 - x)
= 0.1x – 0.3x
= (0.1x – 0.3x) combine like terms
= x subtract 7 both sides = -0.2x simplified
-3.75/ = x divide both sides by -0.2
= x solution
Since x represents the number of liters of the 10% acid solution, the lab technician should use 18.75

15. Essential Questions
When writing an equation to represent a real-world problem situation, how do you determine what the variable will represents?
How are the properties of equality useful when solving the equation?
What do you need to know in order to write a percent as a decimal?
The variable usually represents what you are you trying to find.
They provide the operations needed to get p by it’s self on one side of the equation.

16. Examples 4 & 5 pearsonrealize.com