Label individual bell ringers by date Which of the following mathematical expressions is equivalent to the verbal expression “A number, x, squared is 39 more than the product of 10 and x”? F. 2x = 39 + 10x G. 2x = 39x + 10x H. x2 = 39 – 10x J. x2 = 39 + x10 K. x2 = 39 + 10x Note: Write all bell ringers from a given week on a single piece of paper. Turn this piece of paper in on the last day of the week. Title: Bell Ringers Label individual bell ringers by date

1.2 Properties of Real Numbers In this class there are real numbers and imaginary numbers, for the first 5 units we will only deal with real numbers! We will always start with vocabulary. Only write vocabulary terms you DO NOT know.

Subsets of Real Numbers Natural Numbers Ex. 1, 2, 3, 4 … The numbers used for counting

Subsets of Real Numbers Whole Numbers Ex. 0, 1, 2, 3, 4 … The natural numbers and 0

Subsets of Real Numbers Integers Ex. … -3, -2, -1, 0, 1, 2, 3 … The natural numbers, their opposites, and zero

Subsets of Real Numbers Rational Numbers Ex. 7/5, -3/2, -4/5, 0, 0.3, -1.2, 9 Any number that can be written as a quotient; any number that terminates or repeats

Subsets of Real Numbers Irrational numbers Ex. √2, √7 , √2/3, 1011011101111011111… Numbers that cannot be written as quotients of integers

Subsets of Real Numbers This diagram represents how all the subsets are related.

Graphing numbers on the number line To be able to graph on a number line you need to understand what integers numbers fall between Practice: Name the 2 numbers each number falls between -3/2 = -2 ¼ = 0.33333333…. =

The opposite or additive inverse of any number a is –a The opposite or additive inverse of any number a is –a. The sum of opposites is 0. Practice: ⅙ = -⅝ = -(-3.2) =

The reciprocal or multiplicative inverse of any nonzero a is 1/a The reciprocal or multiplicative inverse of any nonzero a is 1/a. The product of reciprocals is 1. Practice: ⅙ = -⅝ = -(-3.2) =

Finding Absolute Value The absolute value of a real number is its distance from zero on the number line. Practice: Find |-4|, |0|, and |-1(-2)| and graph on a number line.

1.3 Patterns and Expressions Vocabulary: A variable is a symbol, usually a letter, that represents one or more numbers. Ex. x, y, a, b….

Vocabulary continued … Algebraic Expression or a Variable Expression: an expression that contains one or more variables Ex. 3x + 2b *Note: An expression has no equation sign!!!!

Vocabulary continued … Evaluate: When you substitute numbers for the variables in an expression and follow the order of operations to simplify Practice: a – 2b + ab for a = 4 and b = -2

Evaluating Practice –x2 + 3(x – 3) for x = 2

x(4x – x) – x2 for x = -5 and x = -2 Evaluating Practice x(4x – x) – x2 for x = -5 and x = -2

Term: A number, a variable, or the product of a number and one or more variables Coefficient: The numerical factor in a term 5x2 + 6x

Like terms = the same variables raised to the same powers Ex Like terms = the same variables raised to the same powers Ex. 3x2 and 5x2 or -7x3 and 8x3

Combining like terms Practice: 5x2 – 10x + 3x2 -(m + n) + 2(m – 3n)

Finding the perimeter by combining like terms 3x 2x - y y 2x y 3x - y

Practice Evaluate the expression for the given values of the variables. 4a + 7b + 3a – 2b + 2a; a = -5 and b=3

Practice Evaluate the expression for the given value of the variable. |x| + |2x| - |x – 1|; x = 2

Evaluate |2x + 3| + |5 – 3x|for x = -3

Equations with variables on both sides 1.4 Solving Equations Solve 13y + 48 = 8y - 47 Equations with variables on both sides

Practice 8x + 12 = 5x - 21

Practice 2x – 3 = 9 – 4x

Using the Distributive Property 3x – 7(2x – 13) = 3(-2x + 9)

Practice 2(y – 3) + 6 = 70

Practice 6(x – 2) = 2(9 – 2x)

Solving a Formula for One of it’s Variables Solve the formula for the area of a trapezoid for h: A = ½ h (b1 + b2)

Solve the same equation for b1 A = ½ h (b1 + b2)

Homework Study vocabulary terms used in todays class Review sections 1 – 3 from Chapter 1 in your textbook if you need the extra practice

Solving an Graphing Inequalities 1.5 Solving Inequalities Solving an Graphing Inequalities 3x – 12 < 3

Practice 6 + 5(2 – x) < 41

Practice 12 > 2(3x + 1) + 22

Solve each inequality and graph the solution. 2x – 3 > 2(x – 5) Special Cases Solve each inequality and graph the solution. 2x – 3 > 2(x – 5)

Solve each inequality and graph the solution. 7x + 6 < 7(x – 4) Special Cases Solve each inequality and graph the solution. 7x + 6 < 7(x – 4)

Real World Connection Revenue: A band agrees to play for $200 plus 25% of the ticket sales. Find the ticket sales needed for the band to receive at least $500. Write an inequality and solve: 200 + .25x > 500 x > 1200

Practice A salesperson earns a salary of $700 per month plus 2% of the sales. What must the sales be if the salesperson is to have a monthly income of at least $1800? at least $55,000

Compound Inequalities (AND) A compound inequality is a pair of inequalities joined by AND or Or. Example: 3x – 1 > -28 and 2x + 7 < 19

Practice (AND) 2x > x + 6 and x – 7 < 2

Compound Inequalities (OR) 4y – 2 > 14 or 3y – 4 < -13

1.6 Absolute Value Equations and Inequalities The absolute value of a number is its distance from zero on the number line and distance is nonnegative. Example: |2x – 4| = 12

Practice |3x + 2|= 7

Solving Multi-Step AV Equations 3|4x – 1| - 5 = 10

Practice 2|3x – 1| + 5 = 33

Practice |2x + 7| = -2

An extraneous solution is a solution of an equation derived from an original equation that is not a solution of the original equation

Checking for extraneous Solutions |2x + 5| = 3x + 4 Solve like normal Check your answers

Practice |2x + 3| = 3x + 2

Solving Absolute Value Inequalities Solve |3x + 6| > 12. Graph the solution.

Solve 3|2x + 6| - 9 < 15 . Graph the solution. Practice Solve 3|2x + 6| - 9 < 15 . Graph the solution.

Solve |5x + 3| - 7 < 34 . Graph the solution. Practice Solve |5x + 3| - 7 < 34 . Graph the solution.

Bell Ringer The expression (3x – 4y2)(3x + 4y2) is equivalent to:

Bell Ringer The expression -8x3(7x6 – 3x5) is equivalent to: A. -56x9 + 24x8 B. -56x9 - 24x8 C. -56x18 + 24x15 D. -56x18 – 24x15 E. -32x4

Bell Ringer Marlon is bowling in a tournament and has the highest average after 5 games, with scores of 210, 225, 254, 231, and 280. In order to maintain this exact average, what must be Marlon’s score for his 6th game? F. 200 G. 210 H. 231 J. 240 K. 245