Drill #6 Simplify each expression: 1. 2. 2(c + d) – 5(c – 2d) Name the property: 3. a (4 + c) = 4a + ac 4. a + (4 + c) = (4 + c) + a Name the Additive and Multiplicative Inverse: 5. -¾ 6. 2.6
Drill #7 Simplify each expression: 1. 2. –(x + y) – 2(2x – 3y) Translate the following verbal expressions into algebraic expressions 3. The sum of twice a number and four is five less than half the same number. 4. The square of the product of 3 and a number is the same as 3 times the number squared
Drill #8 Solve each equation: 1. 17a = -8 + 9a 2.5(a – 1) = 2(a + 5) 3. 4.
Drill #9 Solve each equation: 1. 2(x + 1) = – 3 ( x – 2) 2. 1 + (3 – x) = 2 – ( x + 1) Solve for the unknown variable: 3. for l 4.for x
Drill #10 Solve each equation: 1. 5(x + 1) = 3( x – 2) + 2x 2. 1 + (2x – 2) = 5 – ( x + 1) Solve for the unknown variable: 3. for x 4.for x
1-3 Solving Equations Objective: Translate verbal expressions into algebraic expressions, and to solve equations using SGIR, and to solve formulas for a given variable.
Verbal to Algebraic Expression: Examples #1. 2 more than 4 times the cube of a number. #2. The quotient of 5 less than a number and 12. #3. The cube of a number increase by 4 times the same number #4. three time the difference of a number and 8
Classwork Copy the following statements, then write an algebraic expression to represent them: #1. The difference between the product of four and a number and 6. #2. The product of a square of a number and 8. #3. Fifteen less than the cube of a number. #4. Five more than the quotient of a number and 4.
Algebraic to Verbal Expression: Examples #1: 6x = 72 #2: n + 15 - 91 #3 g – 5 = -2 #4:
Classwork Write a verbal statement to represent each of the following algebraic expressions: #1: 10x = -5 #2: 2(c + 4) #3 5 – 2 + 18x #4:
Properties of Equality Reflexive Transitive Symmetric Substitution Addition Multiplication
Reflexive property of equality* Definition:For any real number a, a = a.
Transitive Property of Equality* Definition:For all real numbers a, b, and c, if a = b, and b = c, then a = c. Example: if x = y and we know that y = 6 then we also know that x = 6.
Symmetric Property of Equality* Definition: For all real numbers a and b, if a = b then b = a. Example: if y = 5x + 2 then 5x + 2 = y
Substitution Property of Equality* Definition:If a = b, then a may be replaced by b. Example: if x + 5 = 2y + 1 and we know that x = 6, then we can replace x with 6. 6 + 5 = 2y + 1
Addition and Subtraction Property of Equality* Definition: For any real numbers a, b, and ,c if a = b, then a + c = b + c, and a – c = b – c. What you do to one side of an equality you must do to the other.
Multiplication and Division properties of Equality* Definition: For any real numbers a, b, and c if a = b, then a * c = b * c, and if c = 0, a / c = b / c. If 0.1x + 0.25 = 1.1y – 1.6 then 10x + 25 = 110y - 160 What are we multiplying each side by?
S. G. I. R. • implify the expression. (distribute, simplify fractions and decimals) • roup the variables onto one side (the left) of the equation using ADDITION and SUBTRACTION. • solate the variable. Group all non-variable terms (numbers) to the opposite side (the right side) using ADDITION and SUBTRACTION. R. emove the coefficient. Once the variable is isolated the last step is to remove the coefficient. DIVIDE both sides by the coefficient, or MULTIPLY both sides by the reciprocal of the coefficient.
Simplifying Decimals Steps to simplify decimals: 1. Find the smallest decimal (the decimal that goes out the most places). 2. Multiply both side by 10 times 10 (the number of decimal places of the smallest decimal ) (WHY 10?) 1.1x + 2.3 = 5.22
Simplifying Fractions Steps to simplify fractions: 1. Find the least common multiple of all the denominators on both sides of the equation 2. Multiply both sides of the equation (every term) by the LCM
Constants, Variables, Coefficients, and Like Terms* Constant: Any real number Example: 5, 6, 3.23, pi Variable: Letters used to represent numbers that are not known Example: x, y , z, d, s, t Coefficient: The numerical factor of a monomial Example: 4x 4 is the coefficient Like Terms: Terms that have the same variables to the same powers.
No Solution and the Identity* Identity:An equation that is true for all values of a variable. Example: 3x + 2 = 3x + 2 No Solution: An equation that can not be solved. There is no value of the variable that will solve the equation. Example: 3x + 2 = 3x
Steps:Solving for an given variable You use the same steps that you would use to solve an equation to solve for an given variable: • Simplify the Expression • Group the terms with the variable you are solving for onto one side • Isolate the variable: group all other terms on the opposite side • Remove the coefficient…Divide! NOTE: If there is more than one term with the variable in it then factor (undistribute)
Writing Equations:Examples Ex1: The length of a rectangle is 4 less than twice the width. The perimeter of the rectangle is 24. What are the dimensions of the rectangle? Ex2: During a recent season, Miguel Cabrera and Mike Jacobs of the Florida Marlins hit a combined total of 46 homeruns. Cabrera hit 6 more homeruns than Jacobs. How many did each player hit?