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