1.4 Start Thinking. 1.4 Warm Up. 1.4 Cumulative Review Warm Up
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1 1.4 Start Thinking Absolute value is the measurement of the distance from zero on a number line. Use a ruler to construct a number line from 4 to 4 with equal amounts of space between the tick marks. Use your construction to compare the distance from 0 to 4 and from 0 to 4. Explain how this proves the absolute value of 4 and 4 are both equal to Warm Up Determine whether the situation could involve negative numbers. Explain your reasoning. 1. the number of points one team scores in a basketball game. the amount of money in a bank account. the amount of electricity used on this month s bill compared to last month s bill 1.4 Cumulative Review Warm Up Copy and complete the statement using <, >, or =
2 Name Date 1.4 Practice A In Exercises 1 4, simplify the expression In Exercises 5 1, solve the equation. Graph the solution(s), if possible. 5. r = 5 6. q = 7 7. b = 5 8. k + 6 = 9 a 9. 5p = = y = 1 1. x = 1. The minimum distance between two fence posts is 4 feet. The maximum distance is 10 feet. a. Represent these two distances on a number line. b. Write an absolute value equation that represents the minimum and maximum distances. In Exercises 14 19, solve the equation. Check your solutions. 14. j = j f 6 = 9f 16. b + = b 17. 4h = h w 5 = w y + 5 = y 0. Your friend says the absolute value equation x = has two solutions because the constant on the right side of the equation is positive. Is your friend correct Explain. 1. Describe a real-life situation that can be modeled by an absolute-value equation with the solutions x = 5 and x = Algebra 1 Copyright Big Ideas Learning, LLC
3 Name Date 1.4 Practice B In Exercises 1 10, solve the equation. Graph the solution(s), if possible. 1. p = 10. k = 6 q. 6f = 4. = 5 5. a = m = g 1 = 1 8. x + 9 = 0 9. d 6 + = 10. 7c = 11. A company manufactures penny number nails that are 1 inch in length. The actual length is allowed to vary by up to 1 inch. a. Write and solve an absolute value equation to find the minimum and maximum acceptable nail length. b. A penny number nail is 1.05 inches long. Is the nail acceptable Explain. In Exercises 1 14, write an absolute value equation that has the given solutions. 1. and and and 11 In Exercises 15 0, solve the equation. Check your solutions w 4 = w n + 7 = 4n t + 1 = 6t r + = r 19. j 5 = j k + 4 = k + 1. You conduct a random survey of your small town about having a townwide garage sale. Of those surveyed, 56% are in favor and 44% are opposed. The actual percent could be 5% more or 5% less than the acquired results. a. Write and solve an absolute value equation to find the least and greatest percents of your town population that could be opposed to a townwide garage sale. b. A friend claims that half the town is actually opposed to a townwide garage sale. Does this statement conflict with the survey data Explain. 1
4 Name Date 1.4 Enrichment and Extension Extraneous Solutions in Algebra In many algebraic problems, there is the possibility of finding an apparent solution to a problem that does not solve the equation correctly. These solutions are called extraneous solutions. When solving absolute value equations, you see extraneous solutions for the first time, and they continue to come up as you continue through algebra. Solving square root equations is another time when you may find extraneous solutions. Recall that you cannot have a negative value under the radical, and when you take the square root of a number, the answer is never negative. Example: Solve 1 x = x. Check: ( 1 x) x 1 x = x = + x 1 = 0 ( x )( x ) x 1 x = x + 4 = 0 x + 4 = 0 x = 4 x = 0 x = Write the equation. Square each side. Simplify. Write in standard form. Factor. Set each factor equal to zero and solve. ( ) ( ) 1 4 = 4 () 16 = = 9 = = The apparent solution, x = 4is extraneous. So, the only solution of the equation is x =. Solve the equation. Check your answer for extraneous solutions. x + x x = x 4. = 1 x + x +. m = 56 m 4. k + 8 k 4 = k k 5. + x = x n = n 7. y y + = y 1 y 1 8. x = x Algebra 1 Copyright Big Ideas Learning, LLC
5 Name Date 1.4 Puzzle Time Did You Hear About The Two Ducks In A Race A B C D E F G H I J K L M N Complete each exercise. Find the answer in the answer column. Write the word under the answer in the box containing the exercise letter. 5, 9 FEET Simplify the expression. A. 7 B IN 7, 7 THRILL C D , 10 SEVERAL 4 THE, AND OF 14, 7 FAST 17 RESULTED 1 1, 4 TIE Find the value of the variable which satisfies the equation. Check your solution. E. x = 7 F. b = 19 G. w 4 = 11 H. 8e = 4 I. q + 5 = 17 J. 65p = 0 K. c 4 = 7c L. s 11 = s + 9 M. h 8 = h + 10 N. During last year's volleyball season, the coach concluded that the number of points scored in each game could be given by the equation x 7 =. How many points were scored in each game 7 IT, WINNER, 5 AGONY no solution OF 1 WEBBED 7, 15 VICTORY 11, 6 THE 11 SECOND
8.4 Start Thinking. 8.4 Warm Up. 8.4 Cumulative Review Warm Up. List the first 10 terms of the geometric sequence = ( ) n
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.7 Start Thinking Use a graphing calculator to graph the function f ( ) =. Sketch the graph on a coordinate plane. Describe the graph of the function. Now graph the functions g ( ) 5, and h ( ) 5 the same
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.6 Start Thinking Graph the lines = and =. Note the change in slope of the line. Graph the line = 0. What is happening to the line? What would the line look like if the slope was changed to 00? 000? What
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Page 1 of 8 7.6 Solving Radical Equations What you should learn GOAL 1 Solve equations that contain radicals or rational exponents. GOAL 2 Use radical equations to solve real-life problems, such as determining
Example #1: Write an Equation Given Slope and a Point Write an equation in slope-intercept form for the line that has a slope of through (5, - 2).
Algebra II: 2-4 Writing Linear Equations Date: Forms of Equations Consider the following graph. The line passes through and. Notice that is the y-intercept of. You can use these two points to find the
Name Date Period. 1. Which of the following shows 160 as a product of its prime factors? a c b
Name Date Period Practice 2 nd Quarter Cumulative Exam This practice exam mirrors your real exam except that the cumulative is completely multiple choice. Some questions do not require work but most do.
3. If a coordinate is zero the point must be on an axis. If the x-coordinate is zero, where will the point be?
Chapter 2: Equations and Inequalities Section 1: The Rectangular Coordinate Systems and Graphs 1. Cartesian Coordinate System. 2. Plot the points ( 3, 5), (4, 3), (3, 4), ( 3, 0) 3. If a coordinate is
For Integrated Math III Students,
For Integrated Math III Students, Congratulations on the completion of the course of Integrated Math II. In order to be prepared for the next course in August, it is important to work through the attached
SECTION 3.1: Quadratic Functions
SECTION 3.: Quadratic Functions Objectives Graph and Analyze Quadratic Functions in Standard and Verte Form Identify the Verte, Ais of Symmetry, and Intercepts of a Quadratic Function Find the Maimum or
Algebra 1 Keystone Remediation Packet Module 1 Anchor 2
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Give students a few minutes to reflect on Exercise 1. Then ask students to share their initial reactions and thoughts in answering the questions.
Student Outcomes Students understand that an equation is a statement of equality between two expressions. When values are substituted for the variables in an equation, the equation is either true or false.