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Drill #6Simplify 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
5*2121
Drill #7Simplify 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
24*2131
Drill #8
Solve each equation:
1. 17a = -8 + 9a
2. 5(a – 1) = 2(a + 5)
3.
4. )13(24)5(2 xx
2
1
3
12
4
3 xx
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 l4. for x54
22
xyx
wlp
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 xyaxx
yx
65
1893
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 Expressions and their Operations
Verbal Expression Operation
And, plus, sum, increased by, more than
Addition
Minus, difference, decreased by, less than
Subtraction
times, product, of (as in ½ of a number)
Multiplication
Divided by, quotient Division
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.
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: cc
3
1
2
42
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.
S. implify the expression. (distribute, simplify fractions and decimals)
T. roup the variables onto one side (the left) of the equation using ADDITION and SUBTRACTION.
I. 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 FractionsSteps 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
6
1
3
1
4
1x
Constants, Variables, Coefficients, and Like Terms*
Constant: Any real numberExample: 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 monomialExample: 4x 4 is the coefficient
Like Terms: Terms that have the same variables to the same powers. yxyxex 22 2,3:
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)
Solve for a given variable: Examples
xforyxxyEx
xforxyxEx
aforcbaEx
yforyxEx
,2342:4
,2562:3
,543:2
,10054:1
Writing Equations: ExamplesEx1: 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?