Chapter 7 Pre Algebra

Solving Two-Step Equations 1/19 Two operations are required to isolate x Plug and Chug to check your answer

Ask five questions about the inequality: Solving Two Step Equations 1. What is the variable? 2. What is the first operation being done to the variable? 3. What is the inverse operation? 4. What is the second operation being done to the variable? 5. What is the inverse operation?

Work Backwards First—undo any addition or subtraction Second—undo any multiplication or division

Example -2x – 5 = 25 = 30 x = -15 -2(-15) – 5 = 25 30 – 5 = 25 25 = 25 Draw “the road” Example Work Backwards -2x – 5 = 25 Add 5 to both sides + 5 + 5 Simplify x • -2  -2 -5 +5 -2x = 30 Divide both sides by -2 -2 -2 Simplify x = -15 -2(-15) – 5 = 25 Check your answer Plug and Chug 30 – 5 = 25 25 = 25

You Try Solve y – 4 = -12 2 2. –4m + 10 = 30 3. ¼a – 13 = -3

You Try Workbook p 113

Solving Multi-Step Equations 1/20 Simplify (use the distributive property to get rid of parenthesis) Combine like terms Follow steps to solve a two step equation.

Simplify -3( a + 6) 4(3m – 7) -8(5r – 2)

Combine like terms 3d + 4 -12d + 7 5(9n – 4) -15 + 7n 6k + 3 – 2(k – 1)

Solve 8a + 4a = 144 3(n - 2) = 36 -3(2y + 7) = -18

Consecutive Integers Counting by ones---integers (positive and negative whole numbers) that come right after each other. 1, 2, 3 -11, -10, -9 Represented algebraically as n, n+1, n+2

Example The sum of two consecutive integers is 131 n + (n+1) = 131 The sum of four consecutive integers is -22 n + (n+1) + (n+2) + (n+3) = -22

You Try Workbook p 116

Writing Equations 1/28 Homework problems The sale price of a sweater is $48. the price is 20% less than the original price. What was the original price? Elena has $240 in the bank, She withdraws $15 cash each week to pay for piano lessons. How many lessons can she afford with her savings? The perimeter of a rectangle is 64 cm. The length is 4 cm less than twice the width. Find the length and width.

4. Wendy bought a drill at a 10% off sale. The sale price was $75. 60 4. Wendy bought a drill at a 10% off sale. The sale price was $75.60. Find the original price p. 5. Lamar’s summer job is mowing lawns for a landscaper. His pay is $7.50/h. Lamar also makes $11.25/h for any time over 40 hours he works in one week. He worked 40 h last week plus n overtime hours and made $339.38. Home many over time hours did he work? 6. Find two whole numbers with a sum of 15 and a product of 54.

7. A farmer is building a square pen 21 ft on each side 7. A farmer is building a square pen 21 ft on each side. He puts one post at each corer and one post every 3 feet between. How many posts will he use? 8. It takes 8 painters 6 hours to paint the walls of a gym. How many person hours does the job require? How many hours will 12 painter take to paint the gym? 9. Cathy has a collection of dimes and quarters. The number of dimes equals the number of quarters. She has a total of $2.80. How many of each coin does Cathy have?

10. The weight of an object on Venus is about 9/10 of its weight on Earth. The weight of an object an Jupiter is above 13/5 times the weight on Earth. If a rock weights 23ib on Venus, how much would it weight on Earth? If the same rock was on Jupiter, how much would it weigh? 11. Jackson, Petra, and Tyrone went to the beach and collected sea shells over the weekend. Jackson collected s sea shells and Petra and Tyrone each collected 13 fewer that than twice the number of sea shells Jackson collected. At the end of the weekend, they has 94 seashells. How many seashells did each person collect?

Chapter 7 Practice Test 2/1 Show all steps. Show all work The sale price of a coat is $24. the price is 40% less than the original price. What was the original price? 2x + 4 = 12 3(2x -5) = 14 5x - 3 + 2x + 5 = 16 -¼ (16x + 32) +2x = 34 3x + 17 = 5x - 13

Chapter 7 Quiz 2/3 Show all steps. Show all work The sale price of a coat is $31. the price is 70% less than the original price. What was the original price? 3x + 5 = -20 7(3x -5) = 7 9x - 8 + 7x + 6 = 2 -5x + 10 = 2x - 11

Transforming Formulas 2/8 Manipulating an equation to solve for a specific variable Use the properties of equality to transform the equations (p 86, 88, 92, 93 in your book)

Solve the area formula A = lw for w Examples Solve x = y – z for z Solve the distance formula d = rt for rate Solve the perimeter formula p = 2l + 2w for w Solve A = ½ h(a + b) for a

Simple and Compound Interest 2/10 Principal The original amount of money deposited into or borrowed from an account Simple Interest When interest is only calculated on the principal. Formula I = prt Interest = principal x rate x time(years)

Example Find the simple interest after 5 years on a savings account with an initial deposit of $325 and a rate of 2% I = prt I is what we are looking for p is $325 r is 2% t is 5 years

Compound Interest Balance Formula When interest is only calculated on balance. Balance Principal plus interest Formula B = p(1 + r)n Balance = principal x ( 1 + rate) raised to the number of interest periods