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Chapter 2 2.2 1. The surface area of a three-dimensional object is the sum of the areas of the faces. If l represents the length of the side of a cube, write a formula for the surface area of the cube. 2. Given the perimeter P and width w of a rectangle, write a formula to find the length l. 3. Identify the equation that does not belong with the other three. a. N + 14 = 27 b. 12 + N = 25 c. N - 16 = 29 d. N - 4 = 9 4. Determine whether each sentence is sometimes, always, or never true. a. X + X = X b. X + 0 = X 5. Determine the value for each statement below. a. If x - 7 = 14, what is the value of x - 2? b. If n + 8 = -12, what is the value of n + 1 2.3 1. Solve each equation for x. a. ax + 7 = 5 b. c. 2. Determine whether each equation has a solution. a. b. c. 3. Determine whether the following statement is sometimes, always, or never true: The sum of three consecutive odd integers equals an even integer. 2.4 1. Solve 5x + 2= ax - 1 for x. 2. Find the value of k for which each equation is an identity. a. b. 3. Compare and contrast solving equations with variables on both sides of the equation to solving onestep or multi-step equations with a variable on one side of the equation. 2.5 1. Determine whether the following statements are sometimes, always, or never true, if c is an integer. a. The value of is greater than zero b. The solution of is greater than 0 c. The inequality has no solution d. The value of is greater than zero 2. Explain why an absolute value can never be negative. 3. Use the sentence a. Describe the values of x that make the sentence true. b. Translate teh sentence into an equation involving absolute value. 2.6 1. Compare and contrast ratios and rates. 2. If and find the value of 2.7 1. If you have 75% of a number n, what percent of decrease is it from the number n? If you have 40% of a number a, what percent of decrease do you have from the number a? What pattern do you notice? Is this always true? 2. Determine whether the following statement is sometimes, always, or never true: The percent of change is less than 100%. 2.8 1. The circumference of an NCAA women’s basketball is 29 inches, and the rubber coating is inch thick. Use the formula where v represents the volume and r is the radius of the inside of the ball, to determine the volume of the air inside the ball. Round to the nearest whole number. 2. Write a formula for A, the area of a geometric figure such as a triangle or rectangle. Then solve the formula for a variable other than A. 3. Solve each equation or formula for the variable indicated: a. For for x: b. For for y: Chapter 5 5.1 1. Compare and contrast the graphs of a < 4 and a ≤ 4. 2. Suppose Order a, b, c, and d from least to greatest. 3. Write three linear inequalities that are equivalent to y < -3. 4. Explain why x - 2 > 5 has the same solution set as x > 7. 5.2 1. Solve each inequality for x. Assume that a > 0. a. b. c. 2. Determine whether and are equivalent. 3. Explain whether the statement If a > b then is sometimes, always, or never true. 4. How are solving linear inequalities and linear equations similar? Different? 5.3 1. Explain how you could solve -3p + 7 ≥ -2 without multiplying or dividing each side by a negative number. 2. If ax + b < ax + c is true for all real values of x, what will be the solution of ax + b > ax + c? Explain how your know. 3. Solve each inequality for x. Assume that a > 0. a. b. c. 4. Name the inequality that does not belong. Explain. a. b. c. d. 5. Explain when the solution set of an inequality will be the empty set or the set of all real numbers. Show an example of each. 5.4 1. Solve each inequality for x. Assume a is constant and a > 0. a. b. or 2. Create an example of a compound inequality containing or that has infinitely many solutions. 3. Determine whether the following statement is always, sometimes, or never true. The graph of a compound inequality that involves an or statement is bounded on the left and right by two values of x. 5.5 1. The graph of an absolute value inequality is sometimes, always, or never the union of two graphs. Explain. 2. Demonstrate why the solution of is not all real numbers. 3. Explain how to determine whether an absolute value inequality uses a compound inequality with and or a compound inequality with or. Then summarize how to solve absolute value inequalities.