Skill Check 1 Write an algebraic expression to

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

Example 2 What is the solution to 25 = 3(2 x + 2) – 5(2 x + 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 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. – 1. 7 D. – 13. 7

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

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

Example 9 Solve |6 – 4 t| + 5 = 0. |6 – 4 t| + 5 |6 – 4 t| = 0 Original equation = – 5 Subtract 5 from each side. This sentence is never true. Answer: The solution set is .

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