Algebra I Unit 1 Relationships between Quantities Chapter ...missstumpffsclassroom.weebly.com/.../9/6/7/29673113/notes_2.1-2.4.pdf · Algebra I Unit 1 Relationships between Quantities

Algebra I Unit 1 Relationships between QuantitiesChapter 2 Linear Equations

Lesson 2-1 Writing Equations

Objectives: I can translate sentences into equations.

I can translate equations into sentences.

CCSS: A.CED.1, MP.2Example 1: Translate Sentences into EquationsTranslate each sentence into an equation.

a. A number b divided by three is six less than c.

b. Fifteen more than z times 6 is 11 less than y times 2.

Guided Practice 1: Translate Sentences into Equations

Translate each sentence into an equation.

a. Two plus the quotient of a number and 8 is the same as 16.

b. Twenty-seven times k is h squared decreased by 9.

Real-World Example 2: Use the UPS Check Problem Solving Plan

A jellybean manufacturer produces 1,250,000 jellybeans per hour. How many hours does it take to produce 10,000,000jellybeans?

Guided Practice 2: Use the UPS Check Problem Solving Plan

There are 50 members in the North Carolina Senate. This is 70 fewer than the number in the North Carolina House ofRepresentatives. How many members are in the North Carolina House of Representatives?

Example 3: Write a Formula

Translate the sentence into a formula.

The perimeter of a square equals four times the length of a side.

¥ = C- 6

6-2+15=29-11

2+5=1627kth

1,250,00=-10,000,010000000÷ 1250000=8 th

50+70 :XX -70=50

Ro=×

s

s s

Pittss

Guided Practice 3: Write a Formula

Translate the sentence into a formula.

In a right triangle, the square of the measure of the hypotenuse c is equal to the sum of the squares of the measures of thelegs, a and b.Example 4: Translate Equations into SentencesTranslate each equation into a sentence.

a.

b. Guided Practice 4: Translate Equations into Sentences

Translate each equation into a sentence.

a.

b. Example 5: Write a Problem

Write a problem based on the given information.

f = cost of fries

f + 1.50 = cost of burger

Guided Practice 5: Write a Problem

Write a problem based on the given information.

p = Beth’s salary

0.1p = bonus

Lesson 2-2 Solving One-Step Equations

Objectives: I can solve equations by using addition and subtraction.

I can solve equations by using multiplication and division.

AZ tb2=c2

12 minus 2 times × is equala to - 5

.

a Squared plus 3 times B -

equals C divided by 6.

÷bats 25 times a squaredplus 2

.

3 divided by 2 times ✓ minus

t cubed is 132.

÷nyprice

- -John buys 4 burgers

burgerat normal price and

price he has a coupon that

takes off the amountof moneyµ of a Fry .g,y(He spends

CCSS: A.REI.1, A.REI.3, MP.6Example 1: Solve by Adding

Solve

Guided Practice 1: Solve by Adding

Solve each equation.

a. b.

Example 2: Solve by subtracting

Solve

Guided Practice 2: Solve by subtracting

Solve each equation.

a. b.

Example 3: Solve by Multiplying or Dividing

Solve each equation.

a.

b. Guided Practice 3: Solve by Multiplying or DividingSolve each equation.

a.

b.

+12+12h= - 15

+25 +25 13€+87+87 j=@

-102-102 C=@

- 27 - zp k€- 16

- 16 K=@

it z±µ= }→

' #¥k=÷iFk= ¥3

IF@5±stE±I÷Iga=w¥3LIF

← ¥5 r=@

% . } - ty .3z=br2g@

Real-World Example 4: Solve

Ricardo is driving 780 miles to Memphis. He drove about of the distance on the first day. About how many miles didRicardo drive?

Guided Practice 4: Solve

Allison is making a stained glass window. Her pattern requires that one fifth of the glass should be blue. She has 288square inches of blue glass. If she intends to use all of her blue glass, how much glass will she need for the entire project?

Lesson 2-3 Solving Multi-Step Equations

Objectives: I can solve equations involving more than one operation.

I can solve equations involving consecutive integers.

CCSS: A.REI.1, A.REI.3, MP.8Example 1: Solve Multi-Step Equations

Solve each equation. Check your solution.

a.

b. Guided Practice 1: Solve Multi-Step EquationsSolve each equation. Check your solution.

a.

b. Real-World Example 2: Write an equation for the problem. Then solve the equation.Susan had a $10 coupon for the purchase of any item. She bought a coat that was on sale for ½ its original price. Afterusing the coupon, Susan paid $125 for the coat before taxes. What was the original price of the coat?

.

780 (F) =D

-

156.3 =D d=4'5@

[email protected]

" 'Ea=@/

K±9g=-24g K=-@

+6¥,

}9"[email protected],=30 n=e@

tzp - 10=125 the1352+ 10 +10 p=zF@

Guided Practice 2: Write an equation for the problem. Then solve the equation.A music store has sold 3/5 of their hip-hop CDs, but 10 were returned. Now the store has 62 hip-hop CDs. How many werethere originally?

Example 3: Solve a Consecutive Integer ProblemWrite an equation for the following problem. Then solve the equation and answer the problem.Find three consecutive odd integers with a sum of 57.

Guided Practice 3: Solve a Consecutive Integer ProblemWrite an equation for the following problem. Then solve the equation and answer the problem.Find three consecutive integers with a sum of 21.

Lesson 2-4 Solving Equations with the Variable on Each Side

Objectives: I can solve equations with the variable on each side.

I can solve equations involving grouping symbols

CCSS: A.REI.1, A.REI.3, MP.1, MP.5Example 1: Solve an Equation with Variables on Each Side

Solve . Check your solution.

Guided Practice 1: Solve an Equation with Variables on Each Side

Solve each equation. Check your solution.

a.

. -

. 5/2 5/2

62=25×+10 52=25 'x

-10 - 10 z{o=×*@

KITE

.tn/+y+z=57}x=5f#txDtxt4)57×=Yp,,o@3×+66=5.7Xtlxt D + ( Xt2)=2l

3×B¥I¥' @6i7@

- 5C - 5C -

ChuYy=2c If g +567=715 ) -2

8+25=35-2

10£-2g @ }3=33✓

+17A + 7 a

" a±z¥

¥za¥za=t@

b. Example 2: Solve an Equation with Grouping Symbols

Solve . Check your solution.

Guided Practice 2: Solve an Equation with Grouping Symbols

Solve each equation. Check your solution.

a. b.

Example 3: Find Special Solutions

Solve each equation.

a.

b. Guided Practice 3: Find Special Solutions

Solve each equation

.it it-

¥ . ¥ tjtax,±f 7¥ :

X=@A m owow

qq.y.am

-6M¥

6+49 - kq - 42 yustt.FI"¥- 4q - 4g 73 =D

6=8q -42 4g8=g8q @ 30

+42 +42

n8s - luz 18 - 65 85=28 - 6s

A A +10 + to +65 t6s

7h-7=-6

+ -2N ¥,5=2,4-

7h - 7h

-7=-6 - 9h S@+6+6 ÷j÷9gnn=@n m

m n -4*-16=320+44 - 161=320- 40C

-44¥ +80=4,ft8ogo.in#N0s0lu@

a. b.

Standardized Test Example 4: Write an Equation

Find the value of h so that the figures have the same area.

A. 1 C. 4

B. 3 D. 5

Guided Practice 4: Write an Equation

Find the value of x so that the figures have the same perimeter.

F. 1.5 H. 3.2

G. 2 J. 4

Lesson 2-5 Solving Equations Involving Absolute Value

Objectives: I can evaluate absolute value expressions.

I can solve absolute value equations.

m7=5×-5

-5+12×-712 't

,¥=;¥trxby-30=20

-16g12×-12×+30+30 ×=@6yf 50 -16g

No

Solutions !

=12614 flo )( he ) ftp.tzbh

⇒- b 3h = 5Th )

3h= 5h - 10

@

[email protected]=L

=W

2( 2×+2 + × )21×+6 ) =w V2×+12 = 6×+4 3×

#

@ 2×+8=6×8 '-4×-2× - 2× FF

X=2