Drill #2Solve the following equations:Check your solutions!

1. 6x + 5 = -4x + 3

2. 2( y + 2 ) = 2( y – 2 )

3. -3 ( z – 2 ) = 2 ( z + 3 )

4. 3x – 2 = x – (2 – 2x)

1-3 Solving Equations

Objective: Translate verbal expressions into algebraic

expressions, and to solve equations using SGIR

Properties of Equality

Reflexive

Transitive

Symmetric

Substitution

Addition

Multiplication

Reflexive property of equality*

Definition: For any real number a, a = a.

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

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.

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?

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

Solve One Step Equations**

183

2.

208

5.

1.4224.3.

yc

xb

na

Example 1: Solve Multi-Step Equations**

2)13(4)12(2.

6)24(310.

14)1(2)3(5.

xxc

xxb

xxa

Example 2: FormulasPick 3 formulas and solve for one

of the variables

325

9

2

1

22

2

2

222

CFprtIbhA

lwPmcErtd

cbalwhVrC

Why verbal expressions?

Why is it important to know how to translate

math english and english math

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

Example 3: Writing Equations

a. 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?

b. 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?