Skill Check 1) Write an algebraic expression to represent the verbal expression 7 less than a number. Answer: n – 7 2) Write an algebraic expression to represent the verbal expression five more than the quotient of a number and 4.

Unit 1-1: Solving Equations and Absolute Value Equations

Example 1 Solve 53 = 3(y – 2) – 2(3y – 1). 53=3(y – 2) – 2(3y – 1)Original equation 53=3y – 6 – 6y + 2Apply the Distributive Property. 53=–3y – 4Simplify the right side. 57=–3yAdd 4 to each side. –19=yDivide each side by –3. Answer: The solution is –19.

Example 2 What is the solution to 25 = 3(2x + 2) – 5(2x + 1)? A.–6 B. C. D.6

Example 3 Surface area formula Subtract πr 2 from each side. Simplify.

Example 3 Divide each side by πr. 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 Answer: 4.7 Replace x with 4. Multiply 2 and 4 first. Subtract 8 from 6. Add.

Example 6 A.18.3 B.1.7 C.–1.7 D.–13.7

Example 7 Case 1a=b y + 3=8 y + 3 – 3=8 – 3 y=5y=5 Answer: The solutions are 5 and –11. Thus, the solution set is  –11, 5 . Check|y + 3|=8 Case 2a=–b y + 3=–8 y + 3 – 3=–8 – 3 y=–11 |y + 3|=8 ? |5 + 3|=8 ? |8|=8 8=88=8 ? |–11 + 3|=8 ? |–8|=8 8=88=8

Example 8 A.{5} B.{–10, 5} C.{–5, 10} D.{–5}

Example 9 Solve |6 – 4t| + 5 = 0. This sentence is never true. Answer: The solution set is . |6 – 4t| + 5=0Original equation |6 – 4t|=–5Subtract 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 #24, 37, 40, 52, 58, 63 Pg #17, 22, 28, 33, 45