ALGEBRA 1 ~ UNIT 1: SOLVING EQUATIONS & INEQUALITIES …mamajernysclass.weebly.com/uploads/1/2/0/1/... · 1.1B Verbal & Algebraic Inequalities I can: ... Example #2: Twice a number

ALGEBRA 1 ~ UNIT 1: SOLVING EQUATIONS & INEQUALITIES

pg. 1

1.1A Verbal & Algebraic Sentences

I can:

Rewrite verbal sentences as equations.

Rewrite equations as verbal sentences.

Term Definition Picture/Example

Algebraic Sentence

Verbal Sentence

Equation

Formula

Twice

Squared

Cubed

Example #1: The sum of w and v equals the square of y.

Example #2: Three times a number t increased by three is sixty-six.

Example #3: Twice a number x is less than the difference of a and b.

ARE YOU A MASTER??

1. What is the difference between an algebraic expression and a verbal expression?

2. What does an equation have to have?


pg. 2

1.1B Verbal & Algebraic Inequalities

I can:

Rewrite verbal sentences as inequalities.

Rewrite inequalities as verbal sentences.

Term Definition Example(s) Picture

>

<

≥

≤

Example #1: Five times a number is as much as forty-five. Example #2: Twice a number c is less than the sum of a and b.

Example #3: Twice a number x is greater than the difference of a and b.

ARE YOU A MASTER??

1. The difference of x and y are identical to 5 times a number z.

2. The difference of x and y is no more than 5 times a number z.


pg. 3

1.2 Solving One-Step Equations & Inequalities

I can:

Solve equations & inequalities by adding.

Solve equations & inequalities by subtracting.

“MOVE” BY SUBTRACTING

Example #1: 5224 x Example #2: 117 x

Example #3: 2.412 x Example #4: 1423 q

Example #5: 9

7

9

4 x Example #6: nn 13412


pg. 4

“MOVE” BY ADDING

Example #7: 712 x Example #8: 138.6 x

Example #9: 4

1

8

3 x Example #10:

2

1

8

3 x

Example #11: pp 463 Example #12: 821 x

ARE YOU A MASTER??

1. 2.97.2 x 2. 1410 k 3. 4

1)

8

1( x


pg. 5

1.3 Solving One-Step Equations & Inequalities

I can:

Solve equations & inequalities by multiplying.

Solve equations & inequalities by dividing.

“CANCEL” STEP W/DIVISION


Example #3: 8.98.2 x Example #4: x5.335.42


“CANCEL” STEP W/MULTIPLICATION

Example #7: 39

x

Example #8: 63

2x


pg. 6

“CANCEL” STEP W/MULTIPLICATION

Example #9: 23

4 x

Example #10: 39

x

Example #11: 63

2 m Example #12:

4

3

8

1 x

ARE YOU A MASTER??

Which inequality does not have the solution 6x ?

A. 122 x B. 366 x C. 56

5x D.

4

3

8

1 x


pg. 7

1.4 Solving Two-Step Equations & Inequalities

I can:

Solve two-step equations.

Solve two-step inequalities.

Example #1: 14173 x Example #2: 791113 d

Example #3: 7114

x

Example #4: 38152 x

Example #5: 21122

x

Example #6: 212325

9C

ARE YOU A MASTER??

1) 03

212 x 2) 2723 x


pg. 8

1.5 Solving Multi-Step Equations & Inequalities

I can:

Solve multi-step equations.

Solve multi-step inequalities.

Example #1: 53

7

x Example #2: 5.13

2

14

x

Example #3: 10225 xx Example #4: 51915 xx

Example #5: 17132 x Example #6: 13273 xxx


pg. 9

Example #7: xx 4884 Example #8: 123

153

x

Example #9: 89211534 nn Example #10: 22932 x

ARE YOU A MASTER??

a) kk 1812 b) 2313 xx


pg. 10

1.6 Solving for a Given Variable

I can:

Solve for a given variable.

Term Definition Picture/Example Equivalent Equations

Solve for _____

TRUE or FALSE 3 + 2 = 5 is equivalent to 3 = 2 + 5?

TRUE or FALSE 3 + 2 = 5 is equivalent to 3 = 2 – 5?

TRUE or FALSE 3 + 2 = 5 is equivalent to 3 = 5 – 2?

Multiple Choice

Given: 3 + x = 5, which choice is equivalent?

A) 3 = x – 5 B) 3 = 5 – x C) 3 = x + 5 D) 3 = x

Example #1: 5 yx ; for x Example #2: 1274 yx ; for x

Example #3: cbyax ; for y Example #4: cbyax ; for a

ARE YOU A MASTER?? Solve for t:

2

t

rs


pg. 11

1.7 Percents in the Real-World

I can:

Find percents.

Solve real-world problems using percents.

A Percentage is a Special Fraction

The % = “Per ______________________”

47% is simply another way of writing the fraction _____________________.

Example #1: Complete the chart:

PERCENT TO A DECIMAL

35% = 35/100

35% ÷ 100 .35

DECIMAL TO A PERCENT

2/100 = 23%

.23 100 23%

Percentage Fraction

7% 7/100

19% 19/100

83%

3%

15/100

47%

36/100


pg. 12

Example #2: Complete the chart below:

Example #3: Jill obtained a score of 23 out of 32 in a science test. She wants to know what this will be as a

percentage?

Step 1: Write the result as a fraction:

Step 2: Change the fraction into a decimal:

Step 3: Change the decimal into a % by multiplying by 100:

Percentage Decimal Decimal Percentage

27% 0.87

2% 0.08

55% 0.42

5% 0.04

17% 0.71

98% 0.07


pg. 13

Example #4: What percentage of the cars are green?

Step 1: Write the result as a fraction:

Step 2: Change the fraction into a decimal:

Step 3: Change the decimal into a % by multiplying by 100:

Your Turn:

1) What is your quiz percentage if you got 12 out of 25 problems correct?

2) What is your quiz percentage if you got 17.5 out of 31 problems correct?

3) A player scores 4 times out of 9 shots. What is their scoring percentage?

4) A player scores 44 times out of 69 shots. What is their scoring percentage?

5) 12 out of 30 students in this class have blue eyes. What percent of students have blue eyes?

Percent

Red

Green

Black

White

18

41 22

19


pg. 14

How to find Percentage of a Number

Step 1: Change the percentage into a ______________ by dividing by 100 (or moving the decimal 2 left).

Step 2: Change the word ‘of ’ into a sign and multiply.

Example #5: In a survey of 120 students it was found that 20% had an iPhone 5. How many students had the

iPhone 5? (hint: find 20% of 120)

Step 1: Change the percentage to a decimal.

Step 2: Change the word ‘of ’ into a sign and multiply.

Your Turn:

1) 25% of 32

2) 75% of 36

3) 80% of 48

4) 10% of 142

5) 20% of 60

Example #6: You found a pair of jeans you absolutely love. The only issue is they are $90 and that’s over your

budget. The kind lady next to you gave you a 30% off coupon. How much will your pair of jeans be with the

coupon?

Step 1: What is 30% of $90?

Step 2: Let’s take off (subtract) that 30%.

Can anyone think of another way to solve this problem?


pg. 15

ARE YOU A MASTER??

Which is the better deal? Show all work to find the total price for EACH item.

Reminder: Show all work.

Final Price: _______________________ Final Price: _______________________

Dicks Sporting Goods

Price: $39.99

Take 20% off today

only!

MC Sports

Price: $44.95

Take 25% off today only!

Documents

ALGEBRA 1 ~ UNIT 1: SOLVING EQUATIONS & INEQUALITIES …mamajernysclass.weebly.com/uploads/1/2/0/1/... · 1.1B Verbal & Algebraic Inequalities I can: ... Example #2: Twice a number