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Transcript of Algebra 2
Include decimals that terminate.
Include decimals that repeat. Have decimal representations that neither terminate nor repeat.
can not be written as a fraction. Variables: Quantities whose values change. Irrational #'s Rational #'s Integers Whole #'s Natural #'s Graph the real numbers -1/5, √2, 2.6 Graphing Real Numbers on the Number Line b) (3 * 4) * 5 = (4 * 3) * 5 a) 3(g + h) + 2g = (3g + 3h) + 2g Identify the Property Shown Mult. Addition Closure
Distributive Properties of Addition and Multiplication Using an inequality symbol ( < or > ), how do √85 and 8.9 compare? Subsets of the Real Numbers b) You had $150, but you are spending $2 each day. What algebraic expression models this situation? a) Write an algebraic experession models the word phase "one less than the product of six and w" ? EX 1: b) c3 - d/8; for c = 1/4 and d = 1 a) 2r + 5(s + 6) - 1; for r = 3 and s = -9 What is the value of the expression for the given values of the variables? EX 3: d) -(x + 4y) + 5(3x - y) c) 2a2 + 3b2 + 6b2 + 5a2 EX: Simplify by combining like terms. d) -2(y - 1) = -16 + y b) 12b = 18 c) -27 + 6y = 3(y - 3) a) x - 8 = -10 EX: Solve #1 RULE:
WHAT YOU DO TO ONE SIDE, YOU MUST DO TO THE OTHER. d) 2x - 12 + 3x = 2(2x - 6) + x c) 7x + 6 - 4x = 12 + 3x - 8 b) -x + 2(5x -1) = 2(3x + 4) +x a) 1 + 5x -6 = 6x - 5 - x Is the equation sometimes, always, or never true? 37 mi 44 mi 46 mi Essex Highville Dayton Newtown The map shows distances between towns in miles. You and your little friend drive together from Newtown to Essex. You drive first, for a total of 40 miles. Then your little friend drives for 1.5 hours, reaching Essex. What is your friends average rate? c) -n + 6 < 7n + 4 b) 7x +9 > 10x - 12 a) 5y - 8 < 12 EX: Solve i.e.: -3x < 12 Just like solving an equation, only difference is when mult. or div. by a negative, you MUST REVERSE the inequality. e) 6x + 9 < 3 or 3x - 8 > 13 d) -9 < t + 4 < 10 EX: Solve compound inequalities i.e. x > -2 and x < 5 x < -2 or x > 1 deff: Compound Inequalities: 2 inequalities joined by "and" or "or". 2x - 1 = 5 Solving an absolute value equation. Then graph the solution: Absolute Value:
the distance a number is from zero on the number line (distance is always postive). 3 x + 2 - 1 = 8 Extraneous Solutions:
solution derived from original equation that is not a solution to the original equation. x = -3 or x = -1 EX: Decide whether the given number is a solution to the equation. 3x+2 = 4x + 5 5x - 2 = 7x + 14 Solve the equation. 3x - 1 >≤ 5 2x + 4 <≥ 6 Land of Gor There are ALWAYS 2 set-ups EX: Rewrite the absolute value inequality as a compound inequality. Absolute value inequalities 4x + 3 < 5 5x + 10 > 15 3x - 4 <≤ 8 EX: Solve and Graph