Practice Problems. Skills Practice
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1 Practice Problems Skills Practice 1. Solve the following equations for the given variable. Show all steps. Simplify your answers. a) I = Prt Solve for t b) 2x + 3y = 6 Solve for y c) A = B(C + D) Solve for D d) A = p + prt Solve for r e) 6x y 11 Solve for y f) A ) t P( 1 r Solve for P g) C r Solve for C 2 h) 3x 5y = 8 Solve for y i) P = A B C Solve for B j) ax 2 + bx + c = 0 Solve for b.
2 2. Given values: x = 0 x = 1 x = 5 x = 3 x = 5 x = 5 3 a. Which of the given values are in the solution set for x < 3? b. Which of the given values are in the solution set for x -1? c. Which of the given values are in the interval ( 2, )? d. Which of the given values are in the interval (-1, 5]? e. Which of the given values are in the interval 5 < x 3? 3. Complete the table below: Inequality Graph Interval Notation x > 8 x 1 8 x < 12 ( 2, ) (, 6] [1, 3]
3 4. Solve the inequality, showing all steps. Write your answer as an inequality and in interval notation, then graph the solution set on the number line. 4x 2x 12 Interval Notation: Graph: 5. Solve the inequality, showing all steps. Write your answer as an inequality and in interval notation, then graph the solution set on the number line. 14m 8 6m 8 Interval Notation: Graph: 6. Solve the inequality, showing all steps. Write your answer as an inequality and in interval notation, then graph the solution set on the number line. 5( 2a 8) 9a 4 Interval Notation: Graph:
4 7. Solve the inequality, showing all steps. Write your answer as an inequality and in interval notation, then graph the solution set on the number line. 2d > 2 (4 2d) + d Interval Notation: Graph: 8. Solve the equation x = Solve the equation x = Given values: x = 0 x = 1 x = 5 x = 7 x = 3 x = 5 x = 9 a. Which of the given values are in the solution set for x < 5? b. Which of the given values are in the solution set for x 5? 11. Graph the solution set for the inequalities shown below. a. x < 1 b. x 4
5 Applications 12. The area of a triangle is given by the formula A = 1 bh. Solve this equation for h. Show 2 your work. Simplify your answer. 13. The volume of a cylinder is given by the formula V = r 2 h. Solve this equation for h. Show your work. Simplify your answer. 14. The Surface area of a cylinder is given by the formula S = 2 rh + 2 r 2. Solve this equation for h. Show your work. Simplify your answer. 15. Relative change is given by the formula Simplify your answer. R N C. Solve for N. Show your work. C
6 16. Translate each of the given statements into an algebraic inequality. a. A PG-13 movie rating means that your age, a, must be at least 13 years for you to view the movie. b. The cost, C A of renting a car from company A is less expensive than the cost, C B, of renting from company B. c. The sum of the length, L, the width, W, and depth, D, of a piece of luggage to be checked on a commercial airline cannot exceed 61 inches without incurring an additional charge. 17. You have $1200 for your trip to the beach. You estimate that it will cost $160 a day for food, entertainment and hotel, plus $230 round trip air fair. a. Write an inequality that can be used to determine the maximum number of days you can stay at the beach. Clearly indicate with each variable represents. b. Solve the inequality, and interpret your answer in a complete sentence.
7 18. Let p represent the marked price of an item at Toys R Us. Bella s aunt gave her a $20 gift card to Toys R Us for her birthday. a. If sales tax is currently 9%, set up an algebraic inequality to express how much she can spend using her gift card. Clearly indicate what each variable represents. b. Solve the inequality, and interpret your answer in a complete sentence. 19. Your car is worth $2000 at most. It is old. You find out that it needs repairs to pass inspection. The auto shop tells you that the parts cost a total of $520, and the labor cost is $68 per hour. If the repairs are more than the car is worth, you are going to donate the car to charity. a. Write an inequality that can be used to determine the maximum number of hours the mechanic can spend working on your car to help you decide to repair it or donate it. Clearly indicate what each variable represents. b. Solve the inequality, and interpret your answer in a complete sentence.
8 Extension 20. CONVERSION FORMULAS: Complete the table below. Show your work. Simplify your answers. Celsius to Fahrenheit Fahrenheit to Celsius Celsius to Kelvin Kelvin to Celsius K = C Kelvin to Fahrenheit Fahrenheit to Kelvin
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1-1 Practice. Expressions and Formulas. Evaluate each expression. 1. 3(4-7) ( ) (4) [20-2( )]
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1-1 Practice Expressions and Formulas Evaluate each expression. 1. 3(4-7) - 11 2. 4(12-4 2 ) 3. 1 + 2-3(4) 2 4. 12 - [20-2(6 2 3 2 2 )] 5. 20 (5-3) + 5 2 (3) 6. (-2) 3 - (3)(8) + (5)(10) 7. 18 - {5 - [34
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Items on this review are grouped by Unit and Topic. A calculator is permitted on the Algebra 1 A Semester Exam. The Algebra 1 A Semester Exam will consist of two parts. Part 1 will be selected response.
Name Period Date DRAFT
Name Period Date Equations and Inequalities Student Packet 4: Inequalities EQ4.1 EQ4.2 EQ4.3 Linear Inequalities in One Variable Add, subtract, multiply, and divide integers. Write expressions, equations,
3 7 x + 5 = 8. j + 1= 4. Write an algebraic expression for the phrase. Simplify the expression. Solve the equation.
Class: Date: Algebra I: 1st Semester Exam Short Answer Write an algebraic expression for the phrase. 1. 2 times the quantity q minus 3 Simplify the expression. 2. 18 6 3. Write the coordinates of the point
Unit 5 Test Review Systems of Linear Equations Name Class Date
Unit 5 Test Review Systems of Linear Equations Name Class Date Find the mistake - The following problems have been solved HOWEVER there could be a mistake. Each question is worth 3 points: 1pt the mistake,