2) Find three consecutive odd integers such that the sum of the second and twice the third is 7 less than 4 times the first.

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1 ALGEBRA U3 REVIEW SHEET 1) Alvin, Simon, and Teddy are brothers whose ages can be represented by consecutive even integers, with Alvin as the youngest and Teddy the oldest. The sum of the Alvin and Teddy is ten less than three times the age of Simon. Find their ages. ) Find three consecutive odd integers such that the sum of the second and twice the third is 7 less than 4 times the first. 3) Solve and graph the inequality; write the solution in interval notation. 4) If, find 5) If, find if. 6) Solve the equation for in terms of a and c: c( a) 1 = 41

2 7) The graph of the function f is shown at the right. Find: a. f(3) b. f(-8) c. if f() = -3 d. if f() = 6 e. Write the domain in interval notation f. Write the range in interval notation g. Is the graph a function? 8) The function f() is the graph. a) Find f(-) b) If f() = 0, find? c) What is the domain of the function? d) What is the range of the function? e) Is the graph a 1-1 function? 9) A triangle has a perimeter of 153 inches. Side #1 is two inches more than Side #, and Side #3 is 0 more than three times Side #1. Determine the lengths of all 3 sides of the triangle.

3 10) Mona, Lisa, and Steve are pooling their change cups to buy a really nice set of highlighters for their favorite teacher Mrs. Sullivan. Mona has nickels, Lisa has dimes, and Steve has quarters. There is one more than twice as many dimes as nickels, and there are four more quarters than nickels. Together they have $4.60, how many of each coin are there? 11) Match the equations to their corresponding properties: 1 Associative Property of Multiplication a) 1 Commutative Property of Multiplication b) 10(1 + ) = 10(1) + 10() Distributive Property c) 4 0 = 0 Multiplicative Inverse Property d) 18 ( 5) = (18 ) 5 Identity Property of Multiplication e) 9 3 = 3 9 Multiplication Property of Zero f) 41 1 = 41 1) If the function h() represents the number of full hours that it takes a person to assemble sets of tires in a factory, which would be an appropriate domain for the function? (1) {, -,-1, 0, 1,, } (3) { 0,,1,1,,,...} () {0, 1,, 3, } (4) {..., 1,.5,0,1,1.5,,...} 13) Tommy needs to replace his broken kitchen chairs and he does not want to spend more than $135. At a garage sale, the seller has matching chairs marked for $30 each, and also has a matching end table for $50 to complete the set. Tommy wants to purchase the end table and as many chairs as he can without going over his budget, how many chairs can be afford if he also buys the end table?

4 14) Solve the following equations: a) ( 1) b) 5 (4 3) ) Identify the following equations as Linear, Quadratic, or Eponential Justfiy your answer y y y y 9 7 y 6 16) Justify the steps of the following simplified epression using the correct properties. + 5(3a 4b) 7(a + b) + 6 GIVEN + 15a 0b 7a 7b a 7a 0b 7b 8 + 8a 7b 17) State the solution of the following, in interval notation ) On a number line, graph the inequality that is represented by [-8, ).

5 19) A rectangle has a length represented by the epression 6 inches and a width represented by 3 5inches. Epress the area of the rectangle in terms of. 0) Simplify and epress your answer with only with positive eponents z y z y 8 9 1) Simplify and epress your answer with only positive eponents. (ab 3 ) (4a 4 b -6 ) ) Subtract from ) You are creating a frame to surround a rectangular picture. The width and length of the picture are and 0 inches, respectively. The width of the frame around the picture is the same on every side,, as shown. in Write a polynomial that represents the total area of the picture and the frame. 0 in in in