Chapter 2. Solving Linear Equation
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1 Chapter 2 Solving Linear Equation
2 2.1 Square Roots and Comparing Real Numbers I can find square roots and compare real numbers. CC.9-12.N.Q.1
3 Square Root of a Number: Words: If b 2 = a, then b is a square root of a. Example: This Photo by Unknown Author is licensed under CC BY- SA
4 Example: Evaluate the Expression. 1) 36 2) 121 3) 400
5 Real Numbers Venn Diagram
6 Example: Tell whether each of the following numbers is real, rational, integer, whole, or irrational
7 Example: Order the number from least to greatest ,, 3, 12, 16 5
8 Conditional Statements: if-then statement Example: If the number is an integer, then it is rational Rewrite in if-then form: All real numbers are rational numbers *true or false?
9 HOMEWORK: p. 76 #1, 2, 4 28 even, 30 33, 34-39
10 2.3 Solve Two-Step Equations I can solve two-step equations CC.9-12.A.REI.3
11 Things to Remember Goal is to get the variable by itself. Addition and Subtraction are inverse operations. Multiplication and Division are inverse operations.
12 Don t Forget Keep the equation balanced. Whatever you do to one side, you must do to the other. This Photo by Unknown Author is licensed under CC BY-SA
13 How to solve two-step equations: Undo the operations in the reverse order of the order of operations. For example: In order of operations we do multiplication or division first, then addition and subtraction. When solving an equation we do the opposite.
14 Examples: x b 7 b 4
15
16 HOMEWORK: p. 94 #1, 2, 4 34 even, 37-39
17 2.4 Solve Multi-Step Equations I can solve multi-step equations CC.9-12.A.REI.3
18 How to Solve Multi-Step Equations Clear the equation of fractions and decimals. Use the distributive property to remove the parentheses on each side. Combine like terms on each side. Undo addition or subtraction. Undo multiplication or division.
19 3 (2 x 8) 18 5
20 p 2 p 3 6
21 3 4( z 5) 31
22 (3a 1) 14.9
23 HOMEWORK: p. 100 #1, 2, 3 31 odd, 33, 34, 37-39
24 2.5 Solve Equations with Variables on Both Sides I can solve equations with variables on both sides. CC.9-12.A.REI.3
25 Steps to Solve Equations w/ Variables on Both Sides 1) Use distributive property if needed. 2) Combine like terms on both sides. 3) Get variable on one side of the equation, constants on the other side. 4) Solve simplified equation using inverse operations.
26 13 5x 2x 8
27 1 4x 5 (5x 20) 5
28 Number of Solutions: Not every equation has one solution Could have infinitely many solutions (identity) Could have no solution
29 5x 6 5( x 1) 4(3x 2) 2(6x 4)
30 HOMEWORK: p. 107 #1, 2, 3 45 odd, 49, 50
31 2.6 Write Ratios and Proportions I can find ratios and write and solve proportions. CC.9-12.A.CED.1
32 Ratios: a comparison of two integers, a and b where b 0 a to b a:b a b
33 Example: At a carwash fundraiser, 18 ninth grade students and 14 tenth grade students worked the first shift. a) Find the ratio of 9 th graders to 10 th graders. b) Find the ratio of 9 th graders to all students.
34 Proportion: equation that states two ratios are equivalent where b 0 and d 0
35 Solve the proportion 12 3 h 17 Try to practice not using cross products in this section
36 Example: A backpacker hikes 5.5 miles in 2 hours. If the hiking rate remains the same, how far will the backpacker hike in 7 hours? Write and solve a proportion to find the answer.
37 Example: Write the sentence as a proportion. Then solve. 3 is to 8 as x is to 32
38 HOMEWORK: p. 117 #1, 2, 3 43 odd, 47-51
39 2.7 Solve Proportions Using Cross Products I can solve proportions using cross products.. CC.9-12.A.CED.1
40 Cross Products In the proportion, the products a d and b c are called cross products. You can solve a proportion for a missing value by using the Cross Products property. Cross Products Property WORDS NUMBERS ALGEBRA In a proportion, cross products are equal. 2 6 = 3 4 If and b 0 and d 0 then ad = bc.
41 4 12 x n 9 24 n 12 5
42 Vocabulary: Scale drawing: 2 D drawing of an object where dimensions are in proportion to real life Scale: relates models dimensions and actual dimensions (i.e. 1 in: 12 feet)
43 Example: Ship model kits sold at a hobby store have a scale of 1 ft:600 ft. A completed model of the Queen Elizabeth II is 1.6 feet long. Estimate the actual length of the Queen Elizabeth II.
44 HOMEWORK: p. 123 #1, 2, 3 29 odd, 32-39
45 2.8 Rewrite Equations and Formulas I can rewrite equations and formulas. CC.9-12.A.CED.4
46 What is a literal equation? A literal equation is an equation that contains more than one variable. When you solve a literal equation, you are rearranging the equation to isolate a variable.
47 Solve ax + b = c for x Then use the solution to solve 2x + 5 = 11
48 Write 3x + 2y = 8 so that y is a function of x.
49 Example: The area for a rectangle is given by the formula A = lw a) Solve the formula for length, l b) Use the rewritten formula to find the length of a rectangle with area = 351 cm 2 and width = 13 cm
50 HOMEWORK: p. 129 #1, 2, 3 27 odd, 32, 33
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Name: Class: Date: Secondary Math 3 Honors - Polynomial and Polynomial Functions Test Review 1 Write 3x 2 ( 2x 2 5x 3 ) in standard form State whether the function is even, odd, or neither Show your work
Dividing Polynomials
3-3 3-3 Dividing Polynomials Warm Up Lesson Presentation Lesson Quiz Algebra 2 Warm Up Divide using long division. 1. 161 7 2. 12.18 2.1 23 5.8 Divide. 3. 4. 6x + 15y 3 7a 2 ab a 2x + 5y 7a b Objective
Section 9.2 Objective: Students will be able to define and work with irrational numbers.
Lincoln Public Schools Math 8 McDougall Littell Middle School Math Course 3 Chapter 9 Items marked A, B, C are increasing in difficulty. Group A questions are the most basic while Group C are the most