Algebra 2 Unit 1: Number Theory, Equations and Inequalities

Number Theory What are the different types of numbers? Define each of the following: –Reals –Irrational numbers –Natural numbers –Whole numbers –Rational numbers –Integers

Are the following numbers rational or irrational? 5 5/ √5 5 + √7 (√10)/ … (5+ √5)(5- √5) (7+ √5)(5- √5)

Define the Closure Property (hint: look at page 18…) True or false? –Integers are closed under multiplication. –Whole numbers are closed under subtraction. –Rational numbers is closed under addition. –Whole numbers are closed under division.

Linear Equations, Inequalities, & Literal Equations ▲ + ©£ = &+¥. Solve for £.

Solve the following equations. y + 14 = x = 49 -4(b + 7) = -12 7q + q – 3q = a – 5 = ¾ n + 1 = -11 4y – 2n = 9 for y. I = prt for r. Pg 25 #41-62.

Inequalities Solve and graph the following equation and inequalities on a number line. – 2x + 6 = 5x + 20 – 2x + 6 < 5x + 20 – 2x + 6 > 5x + 20 – 2x + 6 < 5x + 20 – 2x + 6 > 5x + 20 –Compare and contrast your solutions and graphs. –Assignment: pg 37 #

Literal Equations and Graphing Solve the following equation and inequalities for y. Then, graph each solution on a coordinate plane (by hand). – 2x + 3y = -12 – 2x + 3y < -12 – 2x + 3y > -12 – 2x + 3y < -12 – 2x + 3y > -12

What does each solution mean? How are the graphs similar? How are the graphs different?