Warm-Up 6

4. Which is correct to say, “The yolk of the egg are white’ or, ‘The yolk of the egg is white’?

2.

1.

3. 𝟏𝟑

What is the opposite of the following?

Warm-Up

6

2.

1.

3. 𝟏𝟑

What is the opposite of the following?

−𝟔

𝟕−𝟏𝟑

4. Which is correct to say, “The yolk of the egg are white’ or, ‘The yolk of the egg is white’?

Neither…The yolk of the egg is yellow!

Profit• Profit is how much extra you make.

• So, Profit equals how much you made minus how much it cost you to pay for bills.

• Profit = Income - Expenses

Profit

Profit = Income - Expenses

Palo sells 40 lasers for $5 each. If a case of 40lasers costs him $75, how much profit was made?

Profit = Income - ExpensesProfit = 40($5) - $75

Profit = $200 - $75Profit = $125

Profit

ABC Company has annual expenses of $3200. If they are to make a profit of $4800 this year, whatincome will they need?

Profit = Income - Expenses$4800 = x - $3200

+ $3200 + $3200

$8000 = xIncome = $8000

Objective

Students will solve linear equations using addition and subtraction

Vocabulary

Solve – When you solve an equation you are trying to find the value of the variable that makes the statement true.

Solution – The value of the variable that makes the statement true. In an equality there is only 1 solution. In an inequality there are many solutions.

Equations

Recall that equations have 2 parts – a left side and a right side separated by the equal sign.

Example

12 + a = 20

Left Side

Separation of the two sides

Right Side

Example #1

k + 5 = 3 - 5 -5 k = -2

1. Write the Equation

2. Subtract 5 from both sides. This is the subtraction property of equality

3. After you subtract 5 from both sides you are left with the isolated variable and its value. In this case -2

Check

Original Problem

k + 5 = 3 - 5 -5 k = -2Check k + 5 = 3(-2) + 5 = 3 3 = 3

1. Write the original equation

2. Substitute the answer in for the variable

3. Simplify

3.1 Solving equations using or

- 9 = 2 + y- 2 -2

- 11 = y

1.

2. 𝒎+𝟗=−𝟒+𝟓𝒎+𝟗=𝟏−𝟗−𝟗𝒎=−𝟖

3.1 Solving equations using or

n - 3 = 10+2

+3 +3 n = 15

n - 3 = 121.

2.−𝟐𝟎=𝒑+𝟑−𝟑−𝟑−𝟐𝟑=𝒑

1. Write an equation where

2. Do #1 except you must use a square root .

3. Do #1 except make

3.1 Solving equations using or

7 = |-6| + b

- 6 - 6 1 = b

7 = 6 + b1.

2. 𝟏𝟑+|𝟐|=𝒑+¿−𝟖∨¿𝟏𝟑+𝟐=𝒑+𝟖𝟏𝟓=𝒑+𝟖−𝟖−𝟖𝟕=𝒑

Conclusion What is the goal in solving an equation? What do we have to do in order to isolate

the x in the following equation:

What is a real life example of this type of equation?

3.1– 3.3 Solving equations 1. Linear Equations (Variable raised to the 1st power & not in or | | symbols) are solved using the same basic steps.

1st Simplify both sides (CLT, distribute, get rid of extra signs & symbols)2nd Move all variables to 1 side.3rd Move all constants to the other.4th Move all coefficients.

• 1 step Step #1

Step #3

3.1– 3.3 Solving equations • 1 step

Step 1

Step 4

• 2 steps Step 1

Step 3

Step 4

3.1– 3.3 Solving equations • Real-life equations

(similar)

D A 3 in

X E 2in F

B 5 in C

• Multi-steps

Step #1

Step #1

Step #1

Step #2

Step #3

Step #4

Subtraction Property of Equality The subtraction property of equality states:

– If you subtract the same number from each side of an equation, the two sides remain equal

Here is what it looks like 7 = 7

If I subtract 3 from both sides the equation both sides will remain equal

7 – 3 = 7 – 3 4 = 4

Note: It doesn’t matter what number you subtract from both sides the ending equation will still be

equal

Addition Property of Equality

The addition property of equality states:– If you add the same number to both sides of an equation,

the two sides will remain equalExample:

7 = 7If I add 3 to both sides of the equation, both

sides will remain equal 7 + 3 = 7 + 3

10 = 10