1.1

Solving Equations

Today’s Learning Targets

I will be abe to

• apply inverse opertions to isolate a variable

• solve multi-step equations in an algebraic proof

• solve application problems using inverses

Open Sentence:

A mathematical statement that contains algebraic expressions and a symbol that compares them

Guess and check method:Is 5 a solution?

• 24 – 3d = 9

• 3x + 4 = 18

• 2w – 7 < 3

• 4 + 3w > 19

EquationAn open sentence that contains the symbol =.

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 EqualitySubtract 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

Polya’s 4 step method:

1. Identify the unknown and write a let statement

2. Write an equation for the situation

3. Solve the equation

4. Answer the question using units

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.

Assignment for 1.1 Due Tuesday

Page 9# 4 – 14 even, 15 – 22 all (skip 19), 24 – 26