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Unit 2: Writing and Solving Linear Equations

Section 1 Day 1: Writing equations by looking at tables PATTERNS show up everywhere in math.

One way to display a pattern is through a table:

What patterns do you see?

Ex 1: The width of a rectangle is 4 inches greater than its length. How can we show the change in width as the length changes?

_____________________________________________________ What happens every time the length changes? Can we set up an equation to match this table?

1 3

2 6

3 9

4 12

2

Ex 2: Kristin got a $20 iTunes gift card for her birthday. Each song costs $0.99. How can Kristen figure out how much is left on her card every time she downloads a song?

___________________________________________________ Let t = Let d = What happens every time Kristin buys a song? Can we set up an equation to match this table? Ex 3: What if you don’t know the equation or a story?

Determine the last value in the output column.

Input Output

3 6

4 7

5 8

6 9

7 10

n

3

Ex 4: What if you don’t know the equation or a story? Determine the last value in the output column.

You try #1 You try #2 The width of a rectangle is Determine the last value 5 times greater than its length. in the output column. Complete the table and write the equation that matches the table.

Input Output

2 5

3 7

4 9

5 11

6 13

n

Input Output

1 2

2 5

3 8

4 11

5 14

n

l w

1 5

10

3 15

4

4

5

Unit 2: Writing and Solving Linear Equations

Section 2 Day 1: Solving One-Step Equations VOCABULARY

TERM TEACHER WORDS STUDENT WORDS OR EXAMPLE

Equation

Solution to an equation

Inverse operations

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Simplify. 1) −8.5 = x + 3.8 2) −9x = −3

3) −2 411

= x − 4 4) − x7= −4

YOU TRY

− 3

2= x + 9

2 −6 = 2

7x

x − 9 = −6 x12

= −11

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63° x°

Unit 2: Writing and Solving Linear Equations

Section 2 Day 2: Solving One-Step Equations & Word Problem Friday

1. In 1673, the Hope diamond was reduced from its original weight by about ______ carats, resulting in a diamond weighing about ______ carats. Write and solve an equation to find how many carats the original diamond weighed. Underline what you know. Circle what you are trying to find out (x): 2. Luis deposited $______ into his bank account. He now has $______. Write and solve an equation to find how much was in his account before the deposit. Underline what you know. Circle what you are trying to find out (x): 3. The angles in each pair are complementary. (Complementary angles add up to ____°) Write and solve an equation to find the value of x. Underline what you know. Circle what you are trying to find out (x):

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4. Lisa earned $5 per hour babysitting her sister. Each week she earned $75. Write and solve an equation to show how many hours she worked each week. Underline what you know. Circle what you are trying to find out (h): 5. Helene’s marching band needs money to travel to a competition. Band members have raised $327. They need to raise a total of $954. Write and solve an equation to find how much more they need. Underline what you know. Circle what you are trying to find out (x):

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Unit 2: Writing and Solving Linear Equations Section 3 Day 1: Combining Like Terms

like terms

same variable

same exponent same side of =

Examples: 1) 4x2 − 3x + 5 − 2x2 2) 3x + 5x2 − 7x + 8 You Try: 3) 5x3 − 7x2 + 6x −11+ 3x2 4) −7x2 + 5x −11+ 8x2 + 3x 5) −3x2 + 2x − 7 + 5x2 6) 11x + 7x2 − 5 +12x + 3x2

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Unit 2: Writing and Solving Linear Equations Section 3 Day 2: Write and solve two-step linear

equations

10 = 2x - 6 1 315 5 5x − =

4x – 3 = 11 2 207n + =

5h – 20 = 8 30 = 2x - 8

8x - 4 = 3 2 1 55 2x − =

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Unit 2: Writing and Solving Linear Equations

Section 3 - Day 3: Write and solve two-step linear equations and distribute

Simplify. 1) − +8 12( )x 2) 3) 4) YOU TRY 2(x + 3) = 10 5(h – 4) = 8 9 = -6(x – 2) -2(3 – d) = 4

3( 1) 7x + = 5( 4) 8x− − =

4 91( )x −

− −12 7( )x 3 10( )x +

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Unit 2: Writing and Solving Linear Equations Section 3 - Day 4: Write and solve two-step linear

equations by combining like terms

TERM TEACHER WORDS STUDENT WORDS OR EXAMPLE

terms

Parts of an addition or subtraction

problem

How many terms? Ex #1 Ex #2 Ex #3 Identify the like terms. Ex #1 Ex #2 Ex #3

coefficient A number multiplied by a variable The number in front

of the letter

27 8 12

49+ − =x 5 3 22 79+ = −x x

389 40 22 7

95 10+ − = − + −x x x x

27 8 12

49+ − =x 5 3 22 79+ = −x x

389 40 22 7

95 10+ − = − + −x x x x

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combining like

terms

Add the coefficient and leave the variable and

exponent the same

5 steps to follow when SOLVING EQUATIONS:

1. Distribute 2. Combine like terms 3. 4. Undo subtraction or addition 5. Undo multiplication or division

SIMPLIFY

1. 9 – 6x – 10 + 12x

2. -12x + 4 – 10 – 7x

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SOLVE BY COMBINING LIKE TERMS

3.

4. x x− + − + =5 3 5 1 2

5. x x− + − = − +2 8 7 10 9

10 8 4 10= − + + −x x

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Unit 2 – Writing and Solving Linear Equations Section 3 Day 5: Write and solve two-step linear

equations – Word Problems - NOTES 1. Riva made a down payment of $2000 on a used car. She has $8,365 left to pay on her car loan. Write and solve an equation to find the amount of the loan. Underline what you know. Circle what you are trying to find out (x). 2. The formula for converting Celsius to Fahrenheit: Normal body temperature is 98.6. What is this in Celsius? Underline what you know. Circle what you are trying to find out (C). 3. Because of taxes, Julie’s take home pay is 63% of her weekly salary. What is Julie’s salary if her take home pay is $896? Underline what you know. Circle what you are trying to find out (x). 4. Solve for x. The sum of the angle measures in any triangle is 180°. Underline what you know. Circle what you are trying to find out (x).

F C= +95

32

250

5+x

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5. Taylor received a $40 gift card from Starbucks for her birthday. Each pumpkin spice latte she buys costs $3.75. Which table best describes b, the balance remaining on the gift card after she buys n lattes? Underline what you know. Circle what you are trying to find out. a) b)

n b

1 $36.25

2 $32.50

5 $28.75

7 $25.00 c) d) 6. What is the perimeter of just the triangle?

What is the perimeter of just the rectangle?

n b

2 $32.50

4 $25.00

6 $18.50

8 $0

n b

1 $36.25

3 $28.75

4 $25.00

7 $13.75

n b

2 $32.50

3 $28.75

5 $20.25

6 $16.50

54

5 5

5

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Unit 2 – Writing and Solving Linear Equations Section 3 Day 6: Write and solve two-step linear

equations – Distribution and Combine Like Terms - NOTES

Simplify. 1) 2(4x − 3)−12 = −10 2) −4(−6x − 3)+ 24 = 12 3) −5(1− 5x)+ 5(−8x − 2) = 0 4) −4x + 2(5x − 6)+ 3x = −39 YOU TRY 2x + 3(x − 3) = 6 5(−1x − 9) +10 =15 2(x + 4)− 6 = 10 −4(3x + 5)+ 4x = 12 6(x + 4)− 4 + 2x = 36 4(x + 2)+ 8x = 56

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Unit 2: Writing and Solving Linear Equations Section 4 Day 1: Write and solve equations with x on both

side 5 steps to follow when SOLVING EQUATIONS:

1. Distribute 2. Combine like terms 3. Collect x’s on one side

• • • •

4. Undo subtraction or addition 5. Undo multiplication or division

COLLECTING X’S ON ONE SIDE VS COMBINING LIKE TERMS 7x – 6 = -4x + 15 7 = 14 – 3x + 21 – 8x 0.5 + 0.3x = 0.7x – 0.3 13 + 8 = 7x + 2x - 3

Ex #3

05 0 3 0 7 0 3. . . .+ = −x x

Ex #4

13 8 7 2 3+ = + −x x

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5x – 2 = 3x + 4

9x – 3x + 4 = 8 + 22 24 – 15x = 6 – 5x – 2

You Try Ex #5

4 5 3 2 12x x x− + = −

You Try

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Unit 2: Writing and Solving Linear Equations Section 4 Day 2: Word Problems

1. Only 25% of all apple varieties are left from Johnny Appleseed’s time. There are 36 varieties left. How many varieties of apples were there originally? Underline what you know. Circle what you are trying to find out (x). 2. An average male takes in 35% of his recommended daily caloric intake from junk food. He takes in 700 calories from junk food. What is his recommended daily caloric intake? Underline what you know. Circle what you are trying to find out (x). 3. The formula for density, mass and volume: The density of aluminum is 25g/cm3. If the volume is 4 cm3, what is the mass? Underline what you know. Circle what you are trying to find out (m). 4. Solve for x. The sum of the angle measures in any pentagon is 540.

d mv

=

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Underline what you know. Circle what you are trying to find out (x).

5. Jennifer is saving money to buy a bike. The bike costs $245. She has $125 saved, and each week she adds $15 to her savings. Write and solve an equation to find how many weeks it will take her to save enough money to buy the bike. Underline what you know. Circle what you are trying to find out (x).

750

3x-1

x

750

650

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Unit 2: Writing and Solving Linear Equations Section 5 Day 1: Write and solve equations with two

different variable Ex 1:

Solve for y. Ex 2:

Solve for y. Ex 3:

Solve for y.

5 2 16y+ = 5 2 16x y+ =

3 6 24y− − = 3 6 24y x− − =

2 3 8y− + = 2 3 8y x− + =

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Solve for y.

8 9 56y x− = − 4 12 20y + =

60 12 5x y= + 3 39y x− =

34 7 2x y= + 4 5 12x y− =