solving linear equations

Solving Linear EquationsYou already know how, but do you know why????

Solve this equation!

•3x + 4 = 31

Why did you do what you did?

• Steps we took to solve the equation:• Subtract 4 from both sides of the

equation• Divide by 3 on both sides of the

equation

Properties of Equality

•Subtraction Property of Equality• If a=b, then a-c=b-c•Division Property of Equality• If a=b and c0, then a÷c=b÷c

Other Properties of Equality

• Reflexive Property of Equality• a=a

• Symmetric Property of Equality• If a=b, then b=a

• Transitive Property of Equality• If a=b and b=c, then a=c

• Addition Property of Equality• If a=b, then a+c=b+c

• Multiplication Property of Equality• If a=b, then ac=bc

• Substitution Property of Equality• If a=b, then b may be substituted for a in any

expression containing a.

Two Column Proofs

• They allow us to provide justifications for our steps of solving equations in an organized and methodical manner.• To justify our answer means to

prove why what we did is correct and works.

Two Column Proofs

STATEMENT JUSTIFICATION

3x + 4 = 31 ?3x = 27 ?x = 9 ?

Now you try!

•Solve and Justify Using a Two Column Proof:

•8x – 1 = 23 – 4x

Practice!!

• Think-Ink-Pair-Share• With each of the next problems, think about

how to solve it and the justifications that are needed. Create a two column proof for the problem.

• You will then pair up with your partner to check each other on the work you did.

• We will then get one person or pair to come up and show how they worked the problem to make sure everyone in the class gets it.

Practice Problems

• 5u + 3 = 48• 3f = 4 + f• - 2 = 6• 12b + 21 = -2b – 21• 5x – 20 = + 8

Literal Equations

•An equation that has no numbers and only has variables.• Examples:• C=2r• A=r2

• V=lwh

Solve the literal equation above for “l”

•V=lwh•What inverse operations are needed to

do this?

Solve the literal equation above for “r”

•A = r2•What inverse operations are needed to

do this?

Real World Applications

•Ms. Rogers and Ms. Bradbury bought 25 total pencils to share with their classes. If Ms. Rogers bought 17, how many did Ms. Bradbury purchase?

Real World Applications

•Ms. Herrington bought 6 shirts for an unknown amount of money each. She also bought a pair of pants that cost her 30 dollars. If her entire purchase cost $60, how much did each of her shirts cost? (Don’t worry about tax here, because she was a smart shopper and went on tax free weekend!)

Homework

• Copy these problems down to do for homework.• You will need to solve each equation for the

variable and create a two column proof to show the justifications to your steps.

• 6r + 4 = -r – 24• + 8 = 2• a + 5 = -5a + 5• PV=nrt (Rearrange for t)• 5p – 14 = 8p + 4

Summarizer

•Match the steps of solving an equation to the justifications for that step.•Then answer the question below.