Solving Two-Step Solving Two-Step EquationsEquations

Section 3.2Section 3.2 3.21-41 odd, 46-51

Arithmetic is numbers you squeeze from your head to your hand to your pencil to your paper till you get the

answer.  ~Carl Sandburg, "Arithmetic"

Addition Property•Adding the same number to each side of an equation produces an equivalent equation•If x-a=b, then x-a+a=b+a, or x=b+a

From yesterday (review)

Subtraction Property•Subtracting the same number to each side of an equation produces an equivalent equation•If x+a=b, then x+a-a=b-a, or x=b-a

Multiplication Property•Multiplying each side of an equation by the same nonzero number produces an equivalent equation

From yesterday (review)

Division Property•Dividing each side of an equation by the same non-zero number produces an equivalent equation

if and a 0, then ,or x x

b a a b x aba a

if and 0,then ,or ax b b

ax b a xa a a

For Problems1. Parenthesis2. Exponents3. Multiplication/Division4. Addition/Subtraction

Order of Operations MUSTBE DONE BACKWARDS when solving an equation

For Equations1. Addition/Subtraction2. Multiplication/Division3. Exponents4. Parenthesis

Because we are working to undo the

arithmetic on the variable we follow the

reverse order of operations

Examples6 6 48x

6

7x

Addition/Subtractio

n first66 42x 6 6

Multiplication/

Division Second

5 1 4x 1

15x

15 3x 5 5

5 3 22x 3

5x

35 25x 5 5

37 5 2x

5 537 3x 7

3 73

7x

Follow these steps to1. Simplify Equation2. (Leave this one blank, we’ll add it later)3. Work to Isolate your variable

1. Opposite Order of Operations1. Addition/Subtraction2. Multiplication/Division3. Exponents4. Parenthesis

4. Check your Solution

Steps for Solving an Equation

Important Reminders

What you do to one side, you do to both sides

You are working to isolate your variable

Examples 6 6 42x

5

11

5x

9 3 100x 327 5x

Examples 6 106x

8 1

5 10 5

x

100 9 10x 4 3 5

6 6 2

x

Using formulas•Example 4, page 143•As a SCUBA diver descends into deeper water, the pressure of the water on the diver’s body steadily increases. The pressure at the surface of the water is 2117 pounds per square foot. The pressure increases at a rate of 64 pounds per square foot for each foot the diver descends. Find the depth at which a diver experiences a pressure of 8517 pounds per square foot.

Practical Example

8517 2117 64 /

sP P rate depth

psf psf psf ft d

Practical Example

If you are getting a new texting plan for 50 dollars a month. And cost .01$ per text.

Write an equation that represents the texting plan

How much would you pay for 2,323 texts?

1. Steps for solving two step equations utilizing reverse order of operations

2. Total is equal to initial plus additional

Most Important Points

Solving Two-Step Solving Two-Step EquationsEquations

Section 3.2Section 3.2 3.21-41 odd, 46-51

Arithmetic is numbers you squeeze from your head to your hand to your pencil to your paper till you get the

answer.  ~Carl Sandburg, "Arithmetic"