- Submitted By: Mrwest808
- Date Submitted: 11/17/2011 11:01 AM
- Category: Technology
- Words: 411
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Chap 6.2 solving equations

Ex 3x=2x+2

3x-2x=2

X=2

x/4-1=x/5

x/4-x/5=1

(1/4 -1/5) x=1

( 5/20-4/20)x=1

1/20x=1

X=20

x/10+2=x/20

solve for y

3x+7y=14

7y=14-3

Y=14-3x/7

Solve for y

4x+9y=27

9y=27-4x

Y= 27-4x/9

Sometime equations has no solution

2x+6=2(x+2)

2x+6=2x+4

6=0+4

2=0

This is false so the original equation has no solution.

Sometimes equations have infinitely many solutions

Ex

2(x+1)=2x+2

0+2=0+2

2=2

No matter what x you plug in, you get a true equation so the original equations has.

6.3 Applications of linear equations

Ex

9 subtracted from 8 times a number is 39

Find the number

Let x = the number

8x-9=39

8x=48

X=6

4 subtracte from 6 times a number is 68

Find the number

Let x= number

6x-4=48

6x=72

X=12

The product of 7 and a number is 91.

7x= 91

X=91/7

X=13

Ex The product of 8 and a number is 184 Find the number.

Let x= number

8x=184

X=184/8=23

Ex the quotient of a number by 13 is 9.

Find the number

Let x=number

x/13=9

x=(13)(9)=17

x=17

The sum of a four and twice a number is 36.

Find the number.

Let x= a number

4+2x=36

2x=32

X=16

Three times the sum of five and a number is 48.

Let x = a number

3(5+x)=48

3x+15=48

3x=33

X=11

6.5 solving linear equations

Now we want to solve for all x satisfying some inequality

Ex x>0

=x|x|x

6.6 solving quadratic equations

We’ve been solving equations that involve like

2x+1=0 Inner eqautions

Or 6x+4=0

Quadratic equation looks like

2x^3+4=o

A biniomail is a n algerbaric expression that has two terms.

Ex: x+1

Ex: x+y

Ex 2x+3

We need to learm how to multiply two binomials

Ex (x+2)(x+3)

The method is called foil

First

Outer

Inner

Last

(2x+4) (2x-1)

4x^2-2x+8x-4

= 4x^2+6x-4