Transcript Equation
Equations Introduction x + b = c ……Interactive Opposite of Mult is Divide a + 3 = 11 …… 6 Q & A ax=c Interactive 2a=10 ….. 6 Q & A 3d + 5 = 32 5s + 7 = 42 ax + b = c …. Interactive ax + b = c …. Click Examples ax + b = c …. 5x – 2 = 2x + 13 7x – 2 = 3x + 18 8x + 7 = 3x + 17 9a + 5 = 3a + 41 6Q&A ax + b = cx + d ax + b = cx + d Interactive 6Q&A Equations 5p – 11 = 33 2a + 1 = 11 7c + 2 = 39 An equation is “maths code” which shows that two sides are equal. In the diagram the weight on the LEFT equal the single weight on the RIGHT 2a = 11 1 a2 a2 4y – 1 = 2y + 11 10 + 4d = 2 – 3d 5s – 1 = 11 - s Equations feature letters. The letters “hide” a value 5 6g – 2 = 3g + 13 Equations The emphasis here is to show a method of solving EQUATIONS The following slides show how Adding becomes Subtracting Multiplying becomes Dividing Change Side Change Sign 17 -5 17 = = 12 12 +5 Change the yellow boxes Complete the 2nd line √ ² C x ÷ a 5 6 7 8 9 + - On 0 1 2 3 4 . = Ans (-) 0 Change Side Change Sign +3 5 5 -5 12 12 +8 90 90 Change Yellow = 8 Example = 8 -3 = 7 = 7 = 98 = 98 Example +5 Change Sign A subtraction sum changed to an addition sum Opposite of add is subtract -8 Opposite of subtract is add √ ² C x ÷ a 5 6 7 8 9 + - On 0 1 2 3 4 . = Ans (-) Type in White Change Sides An addition sum changed to a subtraction sum 0 Change Side Change Sign +9 a a Check a = 26 = 26 +9 Opposite of Subtracting is addition = = 26 Opposite of Adding is subtracting √ ² C x ÷ a 5 6 7 8 9 + - On 0 1 2 3 4 . = Ans (-) New Equation 0 a+b=c a + 7 = 16 a= b + 6 = 11 b= c+4=8 c= d + 9 = 17 d= e + 14 = 22 e= f + 11 = 19 f= 17-7 Start Next Add √ ² C x ÷ a 5 6 7 8 9 + - On 0 1 2 3 4 . = Ans (-) 0 Opposite of Multiply is Divide 8 x4 8 = = 32 32 ÷4 Change the yellow boxes Complete the 2nd line √ ² C x ÷ a 5 6 7 8 9 + - On 0 1 2 3 4 . = Ans (-) 0 Mult becomes Divide Check a 5a = 5 a = 5 + 12 Opposite of Multiplication is Division Start New Equation = + 12 ÷5 1 = 27 Click LHS of equation √ ² C x ÷ a 5 6 7 8 9 + - On 0 1 2 3 4 . = Ans (-) 1 0 ÷ ? on right ax = c 8a = 48 a= 2b = 4 b= 7c = 56 c= 6d = 42 d= 5e = 20 e= 8f = 16 f= √ ² C x ÷ a 5 6 7 8 9 + - On 0 1 2 3 4 . = Ans (-) Start Next 0 3d + 5 = 32 3d + 5 3 3d d Letters to the left = 32 = 32 - 5 = 27 = 27 ÷ Opposite of Change from multiplication is + 5 to -5 division = 27 = 9 Numbers to the right 5s + 7 = 42 5s + 7 5 s s Letters to the left = 42 = 42 - 7 = 35 = 35 ÷ Opposite of Change from multiplication + 7 to - 7 is division = 35 = 7 Numbers to the right Equations Letters to Left 4f = +1 4f 4 f Numbers to Right +9 = 9 = 8 f = 8 -1 = = Opposite of x is ÷ √ ² C x ÷ f 5 6 7 8 9 + - On 0 1 2 3 4 . = Ans (-) b +ve Start Next Equation Clear 0 Add becomes subtract (a) 5f + 3 = 13 5f = 13 – 3 = 10 f = 10 ÷ 5 = 2 (b) 2d + 9 = 23 2d = 23 – 9 = 14 d = 14 ÷ 2 = 7 (c) 8y + 5 = 61 8y = 61 – 5 = 56 y = 56 ÷ 8 = 7 (d) 3g + 2 = 14 g=4 (e) 4s + 5 = 37 s=8 (f) 9u + 7 = 52 u=5 (g) 6b + 9 = 45 b=6 (h) 8k + 11 = 67 k=7 ax + b = c 3a-1=5 a= 2b-1=13 b= 3c+1=19 c= 3d+4=25 d= 3e-2=16 e= 4f+5=17 f= b + or -ve Start √ ² C x ÷ a 5 6 7 8 9 + - On 0 1 2 3 4 . = Ans (-) Next 0 8x + 7 = 3x + 17 8x +7 = 3x Identify letter terms Identify number terms Letters on left + 17 8x + 7 = 3x + 17 8x ++7 7 = 3x + 17 = -7 -3x Letters on left Numbers on the Right Change sign from + to - Change sign from + to - 8x + 7 = 3x + 17 8x +7 = 8x 5x -3x = 3x + 17 + 1710 -7 = 5 x x = 10 10 = Simplify Left Opposite of Mult is Div 17 105x 8x-–73x= = ÷ =2 Simplify Right 5x – 2 = 2x + 13 5x -2 = 2x Identify letter terms Identify number terms + 13 5x – 2 = 2x + 13 5x -2 = 2x + 13 = -2x +2 Letters on left Numbers on the Right Change sign from + to - Change sign from - to + 5x – 2 = 2x + 13 5x -2 = 5x 3x -2x = 2x + 13 + 1315+2 = 3 x x = 15 = Simplify Left Opposite of Mult is Div 13 5x+– 22x= =153x ÷ =5 Simplify Right 7x – 2 = 3x + 18 7x -2 = 3x Identify letter terms Identify number terms + 18 7x – 2 = 3x + 18 7x -2 = 3x + 18 = -3x +2 Letters on left Numbers on the Right Change sign from + to - Change sign from - to + 7x – 2 = 3x + 18 7x -2 = 7x 4x -3x = 3x + 18 20+2 + 18 = 4 x x = 20 = Simplify Left Opposite of Mult is Div 18 == 204x 7x+–23x ÷ =5 Simplify Right 9a + 5 = 3a + 41 9a +5 = 3a Identify letter terms Identify number terms + 41 9a + 5 = 3a + 41 9a +5 = 3a + 41 = -3a -5 Letters on left Numbers on the Right Change sign from + to - Change sign from + to - 9a + 5 = 4a + 41 9a +5 = 9a 6a -3a = 3a + 41 +4136- 5 = 6 x a = 36 = Simplify Left Opposite of Mult is Div 41 = 36 9a-–53a = 6a ÷ =6 Simplify Right Equations Letters to Left 6b = -3 Numbers to Right +9 4b = = = = √ ² C x ÷ b 5 6 7 8 9 + - On 0 1 2 3 4 . = Ans (-) b -ve Start Next Equation Clear 0 ax + b = cx+d 8a-3=5a + 15 a= 3b-4=b + 6 b= 8c-5=5c + 1 c= 4d-1=2d + 5 d= 6e-1=3e + 5 e= 7f-1=5f + 5 f= √ ² C x ÷ a 5 6 7 8 9 + - On 0 1 2 3 4 . = Ans (-) b -ve Start Next 0