Algebra I Chapter 2 Notes Linear Equations

Section 2-1 Writing Equations Ex1) Translate each sentence into an equation. Pay attention to the words is, is as much as, is the same as, is identical to a)Seven times a numbers squared is five times the difference of k and m a)Fifteen times a number subtracted from 80 is 25

Section 2-1 Ex2) Translate the sentence into a formula: the area of a triangle equals the product of ½ the length of the base and the height Ex3) Translate each equation into a sentence a)6z – 15 = 45b)

Section 2-2: Solving One-Step Equations Solution – Equivalent Equations – Property NameSymbolsExample Addition Prop. Of Equality Subtraction Prop. Of Equality Multiplication Prop. Of Equality Division Prop. Of Equality

Section 2-2: Solving One-Step Equations Solution – the value(s) that make an equation true Equivalent Equations – equations that have the same solution Property NameSymbolsExample Addition Prop. Of Equality Subtraction Prop. Of Equality Multiplication Prop. Of Equality Division Prop. Of Equality

Section 2-2 Ex1) Solve the one-step equations and check your answer! a)x – 22 = 54b) y + 63 = 79 c) 3m = -12d) e)f) 5 = -6 + n

Section 2-2 Ex2) Of a group of female students surveyed, 225 or about said they talk on the phone while they watch t.v. How many girls were surveyed?

Section 2-2 Ex3) Solve a)g + 5 = 33b) 104 = y – 67 c)d)

Section 2-3 Solving Multi-Step Equations Ex1) Solve a)11x – 4 = 29b) c) 2a – 6 = 4 d)

Section 2-3 Ex2) Sarah is buying a pair of water skis that are on sale for 2/3 of the original price. After he uses a $25 gift certificate, the total cost before taxes is $115. What was the original price of the skis? Write an equation and solve.

Section 2-3 Consecutive Integers – integers in counting order TypeWordsSymbolsExample Consecutive IntegersIntegers in counting order Consecutive Even Integers Even integers in counting order Consecutive Odd Integers Odd integers in counting order

Section 2-3 Ex3) Write an equation for the following problem, then solve the equation. Find 3 consecutive odd integers with a sum of -51

Section 2-4: Solving Equations with Variables on Both Sides Steps for Solving Equations with Multiple Steps

Section 2-4: Solving Equations with Variables on Both Sides Steps for Solving Equations with Multiple Steps 1. Distribute (get rid of parenthesis) 2. Combine Like terms on the same side of = 3. Get variables together on one side of = 4. Add or subtract the number NOT attached to the variable 5. Multiply or divide the number that IS attached to the variable

Section 2-4 Ex1) Solve a)2 + 5k = 3k – 6b) 3w + 2 = 7w c) 5a + 2 = 6 – 7ad)

Section 2-4: Equations with Grouping Symbols Ex2) a)b) 8s – 10 = 3(6 – 2s) c) 7(n – 1) = -2(3 + n)

Section 2-4: Special Solutions Ex2) Solve a)5x + 5 = 3(5x – 4) – 10xb) 3(2b – 1) – 7 = 6b – 10

Section 2-4 Find the value of x so that the figures have the same area 10cm x cm 6 cm 3cm x cm Find the value of x so that the figures have the same perimeter x 6 x 2x + 2

Section 2-5: Solving Equations Involving Absolute Value Absolute Value – The distance a point is from zero on a number line Ex1) Evaluate a) if m = 4b) if x = 2

Section 2-5 Solve the absolute value equation Ex2) Steps 1.Split the equation into 2 equations, one that = the positive number and one that = the negative number 2. Solve each equation (you will have 2 answers!)

Section 2-5 Ex3) Solve a)b)c)

Section 2-6: Ratios and Proportions Ratio – Proportion – Means-Extremes Property of Proportion Words Symbols Examples

Section 2-6: Ratios and Proportions Ratio – A comparison between two numbers using division (fraction) Proportion – two ratios that are equal Means-Extremes Property of Proportion WordsIn a proportion, the product of the extremes is equal to the product of the means SymbolsIf, and b and d do not equal zero, then ad = bc ExamplesSince, 2(2) = 4(1) or 4 = 4

Section 2-6 Ex1) Determine if the ratios are equivalent. Answer yes or no. a)b)c)

Section 2-6 Ex2) Use cross-multiplication to solve the proportions a)b) c)

Section 2-6 Ex3) The Ramsey Cascades Trail is about inches long on a map with a scale of 3 in = 10 miles. What is the actual length of the trail. Let l represent the length.

Section 2-6 Day 2 The Percent Proportion Use the percent proportion to solve the following. a)15 is what percent of 105? b) What is 35% of 125? c) 23 is 55% of what number?

Chapter 2 Word Problems Draw a picture to represent the situation, then setup an equation and solve. 1) A page of the school yearbook is 8.5 by 11 inches. The left and right margins are 1.5 inches and 2.5 inches, respectively. The space between pictures is 0.5 inches. How wide can each picture be to fit 3 across the width of the page?

Chapter 2 Word Problems (cont.) Draw a picture to represent the situation, then setup an equation and solve. 2) While on business, Carrie drive 80 miles per hour in a car and traveled 300 miles per hour in a plane. She drove twice as many hours as she flew and the total mileage for the trip was 1000 miles. How many hours did she drive?

Chapter 2 Word Problems (cont.) Draw a picture to represent the situation, then setup an equation and solve. 3) A gym charges non-members $15 per day to use the pool. Members pay a yearly fee of $200 and $4 per day to use the pool. Find how many days you must use the pool to justify becoming a member.