Equations

Common Rules Both sides of an equation will still be equal if  The same thing is added to both sides  The same thing is taken away from both sides  Both sides are multiplied by the same number  Both sides are divided by the same number

Simple Equations! x+ 4= 6 x = x+ 4= 6– 4 2 x+ 5= 9 x = x+ 5= 9– 5 4 x– 6= 4 x = x– 6= x– 5= 1 x = x– 5= x– 5 1 =

Easy Equations (Can be solved in your head) a) X + 4 = 6 b) X + 5 = 9 c) X + 3 = 9 d) X + 4 = 5 e) X + 4 = 8 f) X + 6 = 18 g) X – 6 = 4 h) X – 5 = 1 i) X + 3 = 9 j) X – 4 = 5 k) X – 2 = 8 l) X – 6 = 12 m) 2X = 6 n) 2X = 10 o) 3X = 9 p) 3X = 18 q) 5X = 45 r) 8X = 16

Easy Equations Solutions a) X + 4 = 6 X = 2 b) X + 5 = 9 X = 4 c) X + 3 = 9 X = 6 d) X + 4 = 5 X = 1 e) X + 4 = 8 X = 4 f) X + 6 = 18 X = 12 g) X – 6 = 4 X = 10 h) X – 5 = 1 X = 6 i) X + 3 = 9 X = 6 j) X – 4 = 5 X = 9 k) X – 2 = 8 X = 10 l) X – 6 = 12 X = 18 m) 2X = 6 X = 3 n) 2X = 10 X = 5 o) 3X = 9 X = 3 p) 3X = 18 X = 6 q) 5X = 45 X = 9 r) 8X = 16 X = 2

Not So Easy Equations! 2X – 7 = 5 X = 6 6X + 5 = 23 X = X = 25 X = 3 3X + 3 = 2X + 7 X = 4 6x – 2 = 4x + 10 X = 6 6 – 3X = 2 – 5X X = – 2 2(X + 3) = 12 X = 3 3(2X + 1) = 33 X = 5 5(3 – 2X) = 3(4 – 3X) X = 3

Very Simple Equations! 2+ 4= 6 2 – = 9 4 – 5 10– 6= 4 10= – 5= – 5 1 = + 4

Simple Equations! x+ 4= 6 x = x= 6 – 4 2 x+ 5= 9 x = x= 9– 5 4 x– 6= 4 x = x= x– 5= 1 x = x= x– 5 1 = + 4

Fairly Simple Equations! = 8 4 = 4 4 = 12 6 = 6 6 = 15 5 = 5 5 = = 10 = 12 4 = 4 4 = 24 6 = 6 6

Fairly Simple Equations! = 8 x = x 4 = 12 x = x 6 = 15 x = x 5 = 50 x = x 10 = 12 x = x 4 = 24 x = x 6

Still Fairly Simple Equations! 5x + 1= 11 5x = 11 – 1 5x =10 x x = 2 3x + 3= 12 3x = 12 – 3 3x =9 x x = 3 4x – 4= 12 4x = x =16 x x = 4 5x – 6= 34 5x = x =40 x x = 8

Simple(ish) Equations! 5x= + 2x 9 5x =9 – 2x 3x =9 x x = 3 4x= – 3x 21 4x =21 + 3x 7x =21 x x = 3 5x= + 3x 14 5x =14 – 3x 2x =14 x x = 7 A)2x = 25 – 3x B)4x = x C)6x = x D)x = 16 – 3x

Simple(ish) Equations! D) x = 16 – 3x A)2x = 25 – 3x B) 4x = x C) 6x = x

More Simple(ish) Equations! 5x= x + 1 5x=10– 2x– 1 3x=9 x x = 3 x= – 2x 9 – 15 x=9+ 2x+ 15 3x=24 x x= 8 2x= – 3x x=55+ 3x– 10 5x=45 x x= 9 3x= + x x=24– x– 12 2x=12 x x= 6

We’ve solved them. Now lets get ready to make equations! If I think of a number and call it x. What is ?  3 bigger than x x + 3  5 bigger than X x + 5  2 less than X x – 2  4 less than X x – 4  Twice x 2x  4 times x 4x  3 greater than twice x 2x + 3  6 less than 4 times x 4x – 6

We’re ready so: lets make equations! 

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Forming Simple Equations 

Solving Problems with Equations 

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 Johns age is: Jimmys age is: = 15

Solving Problems with Equations  Conors age is: Jacks age is: = 18

Solving Problems with Equations The length of a rectangle is 7cm greater than its breadth, as shown. (x+7) cm x cm (i) Find, in terms of x, the perimeter of the rectangle. x+ x + 7+ x+ x + 7 4x + 14 (ii) If the perimeter is 46cm, find the value of x.

Revision Very Simple Equations! 2+ 4= 6 2 – = 9 4 – 5 10– 6= 4 10= – 5= – 5 1 = + 4

Revision Fairly Simple Equations! = 8 x = x 4 = 12 x = x 6 = 15 x = x 5 = 50 x = x 10 = 12 x = x 4 = 24 x = x 6

Revision More Simple(ish) Equations! 5x= x + 1 5x=10– 2x– 1 3x=9 x x = 3 x= – 2x 9 – 15 x=9+ 2x+ 15 3x=24 x x= 8 2x= – 3x x=55+ 3x– 10 5x=45 x x= 9 3x= + x x=24– x– 12 2x=12 x x= 6

Revision More Simple(ish) Equations with Algebra! 6x= x + 8 6x=20– 2x– 8 4x=12 x x = 3 6x= – 4x 31 – 9 6x=31+ 4x+ 9 10x=45 x x= 4 2(3x + 4)= x 6x = – 4x 31 – 9 6x= x + 8 3(2x – 3) = – 4x 31