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Skill Check 1) Write an algebraic expression to represent the verbal expression 7 less than a number. Answer: nβ7 2) Write an algebraic expression to represent the verbal expression five more than the quotient of a number and 4. Answer: π₯ 4 +5 Unit 1-1: Solving Equations Example 1 Solve ππ β π. ππ = π. ππ Answer: The solution is 2.75. Example 2 Solve π β π π Answer: = ππ The solution is β32. Example 3 Solve 53 = 3(y β 2) β 2(3y β 1). 53 = 3(y β 2) β 2(3y β 1) Original equation 53 = 3y β 6 β 6y + 2 Property. Apply the Distributive 53 = β3y β 4 Simplify the right side. 57 = β3y Add 4 to each side. β19 = y Answer: Divide each side by β3. The solution is β19. Example 4 What is the solution to 25 = 3(2x + 2) β 5(2x + 1)? A. β6 B. C. D. 6 Skill Check Add to Fridayβs Notes Example 5 What is the solution to π π πππ + ππ β π π πππ β ππ = ππ Example 6 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. Assignment Pg. 22-23 #9-17odd #22, 23, #37-41 odd #45, #49 Skill Check Homework Assignment Pg. 22-23 #9- z =53 #11: y = -8 #13- x = -6 #15- a = 3 #17- x = 4 #22 β 4n-6 #23 β 8π₯ 2 #37- y = -3 #39- x = -6 #41 β c = -3 #45#49- πΈ π = 2 π π¦βππ₯βπ π= π₯2 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. β1.7 D. β13.7 Example 7 Case 1 a = b a = βb Case 2 y+3 =8 y + 3 = β8 y+3β3 =8β3 y + 3 β 3 = β8 β 3 y = β11 y=5 Check |y + 3| = 8 ? |5 + 3| = 8 |y + 3| = 8 |β11 + 3| = 8 ? |8| = 8 Answer: ? 8=8οΌ The solutions are 5 and β11. Thus, the solution set is ο»β11, 5ο½. ? |β8| = 8 8 = 8οΌ Example 8 What is the solution to |ππ + π| β π = ππ? A. {5} B. {β10, 5} C. {β5, 10} D. {β5} Skill Check Example 9 Solve |6 β 4t| + 5 = 0. |6 β 4t| + 5 = 0 |6 β 4t| = β5 This sentence is never true. Answer: The solution set is ο. 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. Skill Check Assignment Pg. 30-31 #17-35 odd