Linear Equations

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Linear Equations

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Linear Equations : 

Linear Equations Math project

Some simple examples : 

Some simple examples 8(3x-5)-5(2x-8)=20+4x Solution: 24x-40-10x+40=20+4x 14x=20+4x 10x=20 X=2

More examples : 

More examples An easy one: 3(2x+5)+15=x+85 6x+15+15=x+85 6x+30=x+85 6x=x+55 5x=55 X=11

Linear inequalities : 

Linear inequalities An easy one: 3x-7≤5x-13 3x ≤5x-6 -2x ≤-6 x≥3 because of the minus Line 3 - ∞ + ∞

More examples : 

More examples Solving graphically equations 5+3x≤3+5x f(x)=5+3x g(x)=3+5x x y With x=-1 and With x=0 -1 0 2 5 1 Meeting point =1 X=1 x y -1 0 -2 3

System of Inequalities : 

System of Inequalities A harder example (2·√3-6y)(3y+3)=0 4 2·√3-6y=0 -6y=2√3 y= √3 3 3y+3=0 4 ·3y=-3 12y=-3 y=-0.25 4 ·4

Inequalities : 

Inequalities (x-2)(2x+3)>0 1step: x-2=0 x=2 and 2x+3=0 x=-1.5 2step X-2 2x+3 (x-2)(2x+3) - - + - + + + - + -∞ +∞ 2 -1.5 Solution: x€(- ∞, -1.5) or (2, + ∞)

Extra : 

Extra Example which we did in class, lets see if you remember it. :=) u²+u<0 u(u+1)<0 u=0 u=-1 u u+1 U(u+1) - - + - + + + - + 0 -1 - ∞ + ∞

Last example before the end, Haha : 

Last example before the end, Haha Ha, a good example?Or a simple one? Lets see.... a(c-1)+b(1-c) a(c-1)-b(c-1) (c-1)(a-b) That was easy, wasn‘t it??? You think when I say it is the last example, there will be no other examples????....??? What is in the next slide?????

Last, last example : 

Last, last example Some examples for genies...ha, just kidding... 3t³=⅓∙t 3t³- ⅓∙t=0 9t³-t=0 t(9t²-1)=0 t=0 (3t+1)(3t-1)=0 3t=1 T=⅓ 3t-1=0 T=-⅓

Game : 

Game How much is: 1+1-1+1+1+1-4-1+2-1+10+3-7-6+3+5-8-7+9+2-3-1+0+9-7-2+12-4-4-4-4+5-1-1+1-1=????? Result is:::::: -1

End : 

End No sources.... Only math book and my wookbook and my math knowledge Presentator: David Polman, 10A End, I Hope You Liked It

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