Algebra I
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Transcript of Algebra I
Algebra I
Chapter 2
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 toa) Seven times a numbers squared is five times
the difference of k and m
b) 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 sentencea) 6z – 15 = 45 b)
Section 2-2: Solving One-Step Equations
Solution –
Equivalent Equations – Property Name Symbols Example
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 Name Symbols Example
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 = 54 b) y + 63 = 79
c) 3m = -12 d)
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) Solvea) g + 5 = 33 b) 104 = y –
67
c)d)
Section 2-3 Solving Multi-Step Equations
Ex1) Solvea) 11x – 4 = 29 b)
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
Type Words Symbols Example
Consecutive Integers Integers 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 Steps1.
2.
3.
4.
5.
Section 2-4: Solving Equations with Variables on Both Sides
Steps for Solving Equations with Multiple Steps1. 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) Solvea) 2 + 5k = 3k – 6 b) 3w + 2 = 7w
c) 5a + 2 = 6 – 7a d)
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) Solvea) 5x + 5 = 3(5x – 4) – 10x b) 3(2b – 1) – 7 = 6b – 10
Section 2-4
Find the value of x so that the figures have the same area
10cmx cm
6 cm3cm x cm
Find the value of x so that the figures have the same perimeter
x6
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) Evaluatea) if m = 4 b)
if x = 2
Section 2-5
Solve the absolute value equationEx2)
Steps1. 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) Solvea) b)
c)
Ex4) Write an absolute value equation for the graph with points on 11 and 19 (draw a graph)
Section 2-6: Ratios and Proportions
Ratio –
Proportion –
Means-Extremes Property of ProportionWords
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 ProportionWords In a proportion, the product of the extremes is equal to the product of the means
Symbols If , and b and d do not equal zero, then ad = bc
Examples Since , 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 proportionsa) 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 2-7 Percent of Change
Percent of Change –
Percent of Increase –
Percent of Decrease –
Section 2-7 Percent of Change
Percent of Change – the ratio of the change in an amount to the original amount expressed as a percent
Percent of Increase – when the new number is greater than the original number
Percent of Decrease – when the new number is less than the original number
Section 2-7
Ex1) Determine whether each percent of change is a percent increase or a percent decrease. Then find the percent of change.a) Original: 20 b) Original:
25 Final: 23Final: 17
Section 2-7
Ex2) The total number of passengers on cruise ships increased 10% from 2007 to 2009, how many were there in 2007?
Section 2-7Ex3) Marta is purchasing wire and beads to make jewelry. Her merchandise is $28.62 before tax. If the tax is 7.25% of the total sales, what is the final cost?
Ex4) Since Tyrell has earned good grades in school, he qualifies for the good student discount on his car insurance. His monthly payment without the discount is $85. If the discount is 20%, what will he pay each month?