Post on 03-Jan-2016
3.1-3.2Solving Equations with One and Two Steps
Today’s Learning Targets
I will :• solve two-step equations
• solve multi-step equations in an algebraic proof
• write and solve equations from word problems
Solve equations using inverse operations
to produce equivalent equations.
What are inverse operations?What are equivalent equations?
Properties of Equality
Addition Property of Equality
Add the same number to both sides of the equation to produce an equivalent equation.
Subtraction Property of Equality
Subtract the same number from both sides of the equation to produce an equivalent equation.
Properties of Equality
Multiplication Property of EqualityMultiply both sides of the equation by the same
nonzero number to produce an equivalent equation.
Division Property of Equality
Divide each side of the equation by the same nonzero number to produce an equivalent
equation.
How to show your work…
1.Write the original equation.
2.Use properties of equality to solve the problem
3.Check your work.
Examples:1. x – 9 = 15
2.
3. 4x – 3 = 13
4. 3 - 2
Now, write reasons for each step…
Example: Solve 7(5 – x ) = 14
Equation Explanation Reason
7(5 – x ) = 14
Write original equation
Given
35 – 7x = 14
Multiply Distributive property
-7x = -21
Subtract 35 from each side
Subtraction property of equality
x = 3 Divide each side by -7
Division property of equality
Your turn,
Example: Solve 5(x – 2) = 4
Equation Explanation Reason
Your turn,
Example: Solve 5(x – 2) = 4
Equation Explanation Reason
5(x–2) =4 Write original equation
Given
Your turn,
Example: Solve 5(x – 2) = 4
Equation Explanation Reason
5(x–2) =4 Write original equation
Given
5x-10 =4 Multiply Distributive property
Your turn,
Example: Solve 5(x – 2) = 4
Equation Explanation Reason
5(x–2) =4 Write original equation
Given
5x – 10 =4 Multiply Distributive property
5x = 14 Add 10 to both sides
Addition property of equality
Your turn,
Example: Solve 5(x – 2) = 4Equation Explanation Reason
5(x–2) =4 Write original equation
Given
5x -10 =4 Multiply Distributive property
5x = 14 Add to 10 both sides
Addition property of equality
x = 2.8 Divide both sides by 5
Division property of equality
Farmer’s Market
To rent a booth at the farmer’s market costs $20 per week plus a one-time equipment fee of $85. Find the number of weeks Mr. Vegetable rented a booth if he paid a total of $325.
Function Junction
The output of a function is 9 less than 3 times the input. Write an equation for the function and then find the input when the output is -6.
Money, Money
A bank charges $5.00 per month plus $0.30 per check for a standard checking account. Find the number of checks Justine wrote if she paid $8.30 in fees last month.
Soup and Beans activityWith your partner, complete the activity.
Assignment for 3.1-3.2Page 144-6: #3-31 odd, 37, 38, 40, 41, 43