Moving Straight Ahead - linear relationships

Our work on Investigation 1.2 & 1.3 in Moving Straight Ahead.

Moving Straight Ahead Problem 1.2 & 1.3

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Literal Equations

Practice on simplifying and solving equations and notes on literal equations. Introduction to the formula project as well.

Intro To Formula Project

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Chapter 2-5

We learned about equations and problem solving on Friday.

Define the variable in terms of one another.
You define the thing you are looking for in a variable in relation to the information you already have.

For example,

The length of the rectangle is 6in. more than its width. The perimeter of the
rectangle is 24 in. What is the length of the rectangle?

What are we finding and what is the relation? (Relate)
We're finding the length. The length is 6 in. more than the width.

Now define the variable.
w: width and w+6: length.

Solve (Write)
p=2L+2w
24=2(w+6)+2w.
24=2w+12+2w
24=4w+12
24-12=4w+12-12
12=4w
12/4=4w/4
3=w
The width is 3in. The length is 6in. more than the width, so the length is 9in.

Consecutive Integer Problem

You can find consecutive numbers adding up to a number by the "defining variable in terms of another" way.

For example,

The sum of tree consecutive integers is 147. Find the integers.

Define
n= the first integer
n+1= the second integer
n+2= the third integer

Relate
1st integer plus 2nd integer plus third integer

Write
n + n+1 + n+2 =147
n+n+1+n+2=147
3n+3=147
3n+3 -3=147 -3
3n=144
3n/3=144/3
n=48

Chapter 2- Decimals in Equations

In yesterday's math class, we learned how to deal with unwanted decimals in equations. If you come across a decimal in an equation, and do not feel comfortable using it when solving the equation, then it is easy to transform the decimal into a whole number. An easy way to get rid of decimals is to multiply the decimal by it's greatest place value. For example, 7.8*10=78. Remember, whatever you do to one side you must do to the other so make sure that you multiply all of the terms in an equation if you are to multiply the decimal. Here's an example:
7.8y + 2 = 165.8
7.8y(10)+2(10)=165.8(10) Multiply all terms by 10 to get rid of decimals.
78y+20=1658 Now there are no decimals so you can easily solve the equation.
78y+20-20=1658-20
78y=1638
78y/78=1638/78
y=21
Check:
7.8y+2=165.8
165.8=165.8
Post by Kate M

More equations

How to clear fractions and decimals from equations to make solving easier.

Equation solving

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Solving Equations - Distributive Property

Adding steps for equation solving -

Solving Equations - Distributive Property

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Chapter 2-Solving Equations

Today in algebra 1 we learned the steps to solving an equation. The steps are as followed:

Step 1
Step 2
Step 3-combine like terms on EACH side
Step 4
Step 5-Undo addition or subtraction
Step 6-Undo multiplication or division

Example:
13=y over 3+5
13-5=y over 3+5-5 Subtract 5 from each side
8=y over 3 Simplify
8*3=y over 3*3 Multiply each side by 3
y=24 Simplify

After this you must check your work.

13=y over 3+5
13=24 over 3+5 Substitute y for 24
13=8+5
13=13

For this problem you use steps 5&6.

These are the steps for addition and subtraction. When there is and addition sign subtract the same number that's being added. When there is a subtraction sign add the same number that's being subtracted.
When you are dividing in the equation you want to multiply the same umber that is being divided. When you are multiplying you want to divide the number being multiplied.

Example:

3x-4x+6=-2 Combine like terms(3x-4x)
-1x+6=-2 Simplify
-1+6-6=-2-6 Subtract 6 from each side
-1x=-8 Simplify
---------
-1 -1 Divide by 1 on each side
x=8 Simplify


For this problem you use steps 3,5,&6.

By Kathryn S.

Equation Solving - 2 steps & combining like terms

Day 2 of equation solving.

Equation solving

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