Chapter 7 Pre-Algebra

Bell Ringer Width: 𝒘 Length: 𝒘+𝟏𝟎 Equation: 𝟒𝒘+𝟐𝟎=𝟏𝟎𝟎 Get out yesterday’s homework assignment (7.4) Think of any clarifying questions you may have about 7.1-7.4 Write an equation for the following word problem: The perimeter of the classroom is 100 feet. The length is 10 feet greater than the width. Find the length and the width. Width: 𝒘 Length: 𝒘+𝟏𝟎 Equation: 𝟒𝒘+𝟐𝟎=𝟏𝟎𝟎

Quiz Review

QUIZ TOMORROW!! Sections 7.1-7.4 Homework: Page 393-394, 8-23 Study: Notes Problems from today’s review

Bell Ringer (7.5) Get out your notebook and prepare to take notes on Section 7.5 Prepare to ask questions about the 7-1-7.4 quiz

7.5 – Solving Equations With Variables on Both Sides (Page 371) Essential Question: How is solving an equation with the variable appearing twice on the same side of the equals sign different from solving an equation with the variable appearing on both sides of the equals sign?

7.5 cont. Steps in Solving Equations 1. Remove ( ) 2. Remove fractions or decimals by multiplication 3. Combine like terms 4. Isolate variables to one side 5. Undo + or - 6. Undo x or / 7. Check!! 4. Isolate variables to one side

7.5 cont. Example 1: 3𝑦−20=8𝑦 −3𝑦 −3𝑦 −20=5𝑦 5 5 −4=𝑦 CHECK!!

7.5 cont. Example 2: 𝑞+𝑞+𝑞=𝑞+6 3𝑞=𝑞+6 −𝑞 −𝑞 2𝑞=6 2 2 CHECK!! 𝑞=3

7.5 cont. 7.5 cont. 5 𝑛−3 =2𝑛−6 5 𝑛−3 =2𝑛−6 5𝑛−15=2𝑛−6 −2𝑛 −2𝑛 Example 3: 5 𝑛−3 =2𝑛−6 Example 3: 5 𝑛−3 =2𝑛−6 5𝑛−15=2𝑛−6 −2𝑛 −2𝑛 3𝑛−15=−6 +15 +15 3𝑛=9 CHECK!! 3 3 𝑛=3

7.5 cont. 6 𝑔+3 =−2 𝑔+31 6𝑔+18=−2𝑔−62 +2𝑔 +2𝑔 8𝑔+18=−62 −18 −18 8𝑔=−80 Example 4: 6 𝑔+3 =−2 𝑔+31 6𝑔+18=−2𝑔−62 +2𝑔 +2𝑔 8𝑔+18=−62 −18 −18 8𝑔=−80 CHECK!! 8 8 𝑔=−10

7.5 cont. Example 5:

7.5 - Closure How is solving an equation with the variable appearing twice on the same side of the equals sign different from solving an equation with the variable appearing on both sides of the equals sign? Twice on same side: Combine terms using the operation shown On both sides: Combine terms using inverse operations

Page 373-374, 4-22 even, 28, 30 7.5 - Homework

𝒙>𝟒 Bell Ringer (7.6) Get out your 7.5 homework assignment Get out your notebook and prepare to take notes on Section 7.6 Solve the following equation for x: 2𝑥>8 𝒙>𝟒

7.6 – Solving Two- Step Inequalities (Page 377) Essential Question: How is solving two-step inequalities different from solving two-step equations?

7.6 cont. = ≤, ≥ = <, > Graphing Inequalities: We can use the number line to solve inequalities containing < , ≤ , > , and ≥ . = ≤, ≥ = <, >

7.6 cont. 2𝑦−3≤−5 +3 +3 2𝑦≤−2 2 2 𝐲≤−𝟏 Example 1: Solve and graph 2𝑦−3≤−5. 2𝑦−3≤−5 +3 +3 2𝑦≤−2 2 2 𝐲≤−𝟏

7.6 cont. −5𝑦+3≥28 −3 −3 −5𝑦≥25 −5 −5 𝒚≤−𝟓 Example 2: Solve −5𝑦+3≥28. **Remember to reverse the direction of the inequality symbol when you multiply or divide by a negative number**

Therefore, the greatest number of rides Dale can ride is 14. 7.6 cont. Example 3: Dale has $25 to spend at a carnival. If the admission to the carnival is $4 and the rides cost $1.50 each, what is the greatest number of rides Dale can go on? 1.5x+4≤25 Therefore, the greatest number of rides Dale can ride is 14. −4 −4 1.5𝑥≤21 1.5 1.5 𝒙≤𝟏𝟒

7.6 - Closure How is solving two-step inequalities different from solving two-step equations? Same except when you multiply or divide each side of an inequality by a negative number, you must also reverse the inequality symbol.

7.6 - Homework Page 379, 4-24 even, 34, 35

Bell Ringer (7.7) −𝟔𝒚+𝟑≥𝟐𝟕 −𝟔𝒚≥𝟐𝟒 𝒚≤−𝟒 Get out your 7.6 homework assignment Get out your notebook and prepare to take notes on Section 7.7 Solve the following inequality for y: −6𝑦+3≥27 −𝟔𝒚+𝟑≥𝟐𝟕 −𝟔𝒚≥𝟐𝟒 𝒚≤−𝟒

7.7 – Transforming Formulas (Page 382) Essential Question: What does it mean to “solve a formula for a given variable”?

NOT THE RACE CAR BRENDEN!! 7.7 cont. Formula: An equation that shows a relationship between quantities that are represented by variables NOT THE RACE CAR BRENDEN!! BEITZ RACING

7.7 cont. 𝐴=𝑙𝑤 𝑤 𝑤 𝐴 𝑤 =𝑙 Transforming in One Step: Example 1: Solve the area formula for length. 𝐴=𝑙𝑤 𝑤 𝑤 𝐴 𝑤 =𝑙

7.7 cont. 𝑃=2𝑙+2𝑤 −2𝑙 −2𝑙 𝑃−2𝑙=2𝑤 2 2 1 2 𝑃−𝑙=𝑤 Transforming in More Than One Step: Example 2: Solve the perimeter formula for width. 𝑃=2𝑙+2𝑤 −2𝑙 −2𝑙 𝑃−2𝑙=2𝑤 2 2 1 2 𝑃−𝑙=𝑤

7.7 cont. Transforming Temperatures: Example 3: Convert 32℃ to ℉ by solving 𝐶= 5 9 𝐹−32 for F, then substituting. 𝑪= 𝟓 𝟗 𝑭− 𝟏𝟔𝟎 𝟗 𝑭= 𝟗 𝟓 𝑪+𝟑𝟐 𝑪+ 𝟏𝟔𝟎 𝟗 = 𝟓 𝟗 𝑭 𝑭= 𝟗 𝟓 𝟑𝟐 +𝟑𝟐 𝟗𝑪+𝟏𝟔𝟎=𝟓𝑭 𝑭= 𝟐𝟖𝟖 𝟓 +𝟑𝟐 𝑭= 𝟗 𝟓 𝑪+𝟑𝟐 𝑭=𝟖𝟗.𝟔

7.7 - Closure What does it mean to “solve a formula for a given variable”? Expressing one variable in terms of the other variables used in the formula

7.7 - Homework Page 384, 4-26 even

Bell Ringer (7.8) Get out your 7.7 homework assignment Get out your notebook and prepare to take notes on Section 7.8 What does the term “interest” mean in mathematics?

7.8 – Simple and Compound Interest (Page 386) Essential Question: What is the difference between simple interest and compound interest?

7.8 cont. New Vocabulary: Principal – initial amount of an investment or loan Interest - fee charged by a lender to a borrower for the use of borrowed money Interest Rate – percentage of the balance that an account or investment earns in a fixed period of time

7.8 cont. New Vocabulary: Simple Interest – interest paid only on the principal

7.8 cont. 𝐼=𝑝𝑟𝑡 𝐼= 1000 .06 2 𝐼=120= ONLY INTEREST!! Example 1: Suppose you deposit $1,000 in a savings account that earns 6% interest per year. Find the interest earned in 2 years. Find the total principal plus interest. SIMPLE INTEREST PROBLEM!! 𝐼=𝑝𝑟𝑡 𝐼= 1000 .06 2 𝐼=120= ONLY INTEREST!! $1,000+$120=$1,120

7.8 cont. Balance – principal plus earned interest Interest Period – length of time over which interest is calculated Can be a year or less than a year

7.8 cont. Compound Interest – interest paid on both the principal and the interest earned in previous interest periods

7.8 cont. OR 𝐵=𝑝 1+𝑟 𝑛 $𝟓𝟗𝟎.𝟗𝟖 𝐵=400 1+.05 8 𝐵=486.2 1+.05 4 𝐵=590.98 Example 2: Suppose you deposit $400 in an account that earns 5% interest compounded annually. The balance after the first four years is $486.20. What is the balance in your account after another 4 years, a total of 8 years? COMPOUND INTEREST PROBLEM!! 𝐵=𝑝 1+𝑟 𝑛 𝐵=400 1+.05 8 𝐵=590.98 𝐵=486.2 1+.05 4 𝐵=590.98 OR $𝟓𝟗𝟎.𝟗𝟖

7.8 cont.

$𝟐𝟖𝟏𝟔.𝟐𝟑 7.8 cont. 𝐵=𝑝 1+𝑟 𝑛 𝐵=2500 1+.015 8 𝐵=2816.23 Example 3: Find the balance on a deposit of $2,500 that earns %3 interest compounded semiannually for 4 years. 𝐵=𝑝 1+𝑟 𝑛 𝐵=2500 1+.015 8 𝐵=2816.23 $𝟐𝟖𝟏𝟔.𝟐𝟑

7.8 cont.

7.8 - Closure What is the difference between simple interest and compound interest? Simple Interest: Paid only on the principal Compound Interest: Paid on both the principal and the previously earned interest

7.8 - Homework Page 389, 2-18 even

Bell Ringer Get out your 7.8 homework assignment Think of any clarifying questions you may have about Chapter 7 Find the balance on a deposit of $1000 that earns 4% interest compounded semiannually for 5 years.

Steps for Solving Equations: 1. Remove ( ) 2. Remove fractions or decimals by 𝒙 3. Combine like terms 4. Isolate variables to one side 5. Undo + or − 6. Undo × or ÷ 7. Check!!

7.1 - Review (Page 393)

7.2, 7.3 - Review (Page 393)

7.4 - Review (Page 394)

7.5 - Review (Page 394)

7.6 - Review (Page 394-395)

7.7 - Review (Page 347)

7.8 - Review (Page 395)

7.8 – Review cont. (Page 395)

TEST TUESDAY!! Sections 7.1-7.8 Homework: Page 396, 2-42 even Study: Notes Problems from today’s review