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Skill Check 1) Write an algebraic expression to represent the verbal expression 7 less than a number. Answer: nā7 2) Write an algebraic expression to represent the verbal expression five more than the quotient of a number and 4. Answer: š„ 4 +5 Unit 1-1: Solving Equations and Absolute Value Equations Example 1 Solve 53 = 3(y ā 2) ā 2(3y ā 1). 53 = 3(y ā 2) ā 2(3y ā 1) Original equation 53 = 3y ā 6 ā 6y + 2 Property. Apply the Distributive 53 = ā3y ā 4 Simplify the right side. 57 = ā3y Add 4 to each side. ā19 = y Answer: Divide each side by ā3. The solution is ā19. Example 2 What is the solution to 25 = 3(2x + 2) ā 5(2x + 1)? A. ā6 B. C. D. 6 Example 3 Surface area formula Subtract Ļr 2 from each side. Simplify. Example 3 Divide each side by Ļr. Simplify. Example 4 GEOMETRY The formula for the perimeter of a rectangle is where P is the perimeter, and w is the width of the rectangle. What is this formula solved for w? A. B. C. D. Absolute Value Example 5 Replace x with 4. Multiply 2 and 4 first. Subtract 8 from 6. Add. Answer: 4.7 Example 6 A. 18.3 B. 1.7 C. ā1.7 D. ā13.7 Example 7 Case 1 a = b a = āb Case 2 y+3 =8 y + 3 = ā8 y+3ā3 =8ā3 y + 3 ā 3 = ā8 ā 3 y = ā11 y=5 Check |y + 3| = 8 ? |5 + 3| = 8 |y + 3| = 8 |ā11 + 3| = 8 ? |8| = 8 Answer: ? 8=8ļ¼ The solutions are 5 and ā11. Thus, the solution set is ļ»ā11, 5ļ½. ? |ā8| = 8 8 = 8ļ¼ Example 8 What is the solution to |šš + š| ā š = šš? A. {5} B. {ā10, 5} C. {ā5, 10} D. {ā5} Example 9 Solve |6 ā 4t| + 5 = 0. |6 ā 4t| + 5 = 0 |6 ā 4t| = ā5 This sentence is never true. Answer: The solution set is ļ. Original equation Subtract 5 from each side. Example 10 Money The U.S. Mint produces quarters that weigh about 5.67 grams each. After the quarters are produced, a machine weighs them. If the quarter weighs 0.02 grams more or less than the desired weight, the quarter is rejected. Write and solve an equation to find the heaviest and lightest quarters the machine will approve. Assignment Pg. 22-24 #24, 37, 40, 52, 58, 63 Pg. 30-31 #17, 22, 28, 33, 45