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.

Algebraic to Verbal Expression: Examples

#1: 6x = 72

#2: n + 15 - 91

#3 g – 5 = -2

#4: 42

12 2 cc

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

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?

Properties Examples: 1-3 Skills Practice # 11-14

Solve Equations using S.G.I.R*

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

Example 3:One Step Equations**

183

2.

208

5.

1.4224.3.

yc

xb

na

Example 4: Solve Multi-Step Equations**

2)13(4)12(2.

6)24(310.

14)1(2)3(5.

xxc

xxb

xxa

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

Formulas

325

9

2

1

22

2

2

222

CFprtIbhA

lwPmcErtd

cbalwhVrC

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?