Solving Equations X + 3 = 10 4y = 12 2x + 3 = 13 y x15 2x + 3 = 11 y – 4 = 7 Great Marlow School Mathematics Department

Solving an equation is like keeping a scale balanced. x12Here we can see that x = 12 because the scale is balanced. Great Marlow School Mathematics Department

x + 37 On this scale x + 3 = 7 The scale is balanced. But if I take the 3 off… x The scale is not balanced any more. Great Marlow School Mathematics Department

x 7 I can balance it again by taking 3 away from the x This should be written like this to show all the steps needed to work out the answer. X + 3 = = -3 X = 4 Great Marlow School Mathematics Department

y - 25 On this scale y – 2 = 5 Great Marlow School Mathematics Department

If I add 2 to the -2 it will become 0. Then the “y” will be on its own, but the scale will not be balanced. Y (– 2 + 2) 5 Remember ( = 0.) Great Marlow School Mathematics Department

Y – 2 = = + 2 Y = 7 Y (– 2 + 2) 5 How can I balance the scale? Yes, add 2 to the other side of the scale. y 7 It should be written like this. Great Marlow School Mathematics Department

Now you try some. Remember to show all the steps. 1) x + 3 = = - 3 x = 5 2) x + 7 = = - 7 x = 8 3) Y + 5 = = - 5 y = 4 4) z + 5 = = - 5 z = 7 5) a + 4 = = - 4 a = 11 6) Y - 6 = = +6 y = 20 7) d -5 = = + 5 d = 13 8) x - 6 = = + 6 x = 21 9) Y + 13 = = - 13 y = 11 Great Marlow School Mathematics Department

Here 3y = 21 Remember that 3y means 3 X y 3y21 I can’t take the 3 away because it has not been added to the “y”. I must divide the 3y into 3 equal pieces, each piece being 1y. Great Marlow School Mathematics Department

21 3y 3 What’s wrong? Correct – it is not balanced. How can I balance the scale? That’s right – divide 21 into three equal pieces. 3 y 7 21 Great Marlow School Mathematics Department

It should be written like this. 3y = 21 3 y = 7 Great Marlow School Mathematics Department

How do you think we can solve this equation? Y 212 In this equation y divided by 2 equals 12. Great Marlow School Mathematics Department

Y 2 12 Correct! Multiply both sides by 2 X 2X 2 X 2X 2 Remember, if you make a change on one side of the equation, you must make the same change on the other side to keep the equation balanced. y 24 Great Marlow School Mathematics Department

Now you try some. 1)3 a = 184) 2b = a = 6 b = 3.5 2) 5x = 30 5) 7y = x = 6y = 9 3) 6z = 42 6) 4d = z = 7d = 12 7) z = 4 5 z x 5 = 4 x 5 5 z = 20 8) y = 3 8 y x 8 = 3 x 8 8 y = 24 Great Marlow School Mathematics Department

2x If we knew what 2x was equal to the we could work out what 1x was equal to. What do we need to get rid of? Correct – the +3 Great Marlow School Mathematics Department

2x x -3 Take 3 away from both sides. 16 Now 2x = 16 x 8 Divide both sides by 2. 2x + 3 = = -3 2x = X = 8 Any questions?

5x + 3 = = -3 5x = X = 9 6x + 9 = = -9 6x = X = 5 2x - 3 = = +3 2x = X = 11 7x - 6 = = +6 7x = X = 5 3x + 5 = = -5 3x = X = 4 4x -5 = = +5 4x = X = 6 1)2) 4) 3) 5) 6) Great Marlow School Mathematics Department

5x + 32x + 15 This time there are x’s on both sides of the balance. Any suggestions? We could take the 2x off both sides 153x + 3 Now it is just like the previous equations. 5x + 3 = 2x x = -2x 3x + 3 = = -3 3x = X = 4 Great Marlow School Mathematics Department

4x + 2 = 2x x = -2x 2x + 2 = = -2 2x = X = 7 6x + 8 = 3x x = -3x 3x + 8 = = -8 3x = X = 5 7x - 10 = 5x +4 -5x = -5x 2x - 10 = = +10 2x = X = 7 5x + 14 = 7x +3 -5x = -5x 14 = 2x = = 2x = x or x = 5.5 9x - 5 = 2x x = -2x 7x - 5 = = +5 7x = X = 3 3x + 8 = x +15 -x = -x 2x + 8 = = -8 2x = 7 22 X = 3.5 Great Marlow School Mathematics Department

National curriculum reference: A3d Date: June 1995 Paper: The perimeter of this triangle is 31 cm. Work out the value of c. 2c-3+2c+3+4c-5=31 2c+2c+4c-3+3-5=31 8c-5=31 +5=+5 8c = c =4.5 Great Marlow School Mathematics Department

Date: June 1997 Paper: (a)Solve 3x = 24 (b)Solve y = 6 - y. [4] Date: June 1999 Paper: (a)Solve the equation 2x = 10. x = (1 mark) (b)Solve the equation 6y + 1 = 25. y = (2 marks) (c)Solve the equation 8p - 3 = 3p p = (2 marks) See the next slide for the answers. Great Marlow School Mathematics Department

3x = X = y = 6 – y +y = +y y = = -18 4y = Y = -3 2x = y + 1 = = -1 6y = 24 X = 5 Y = p – 3 = 3p p = -3p 5p – 3 = = +3 5p = p = 3.2 or 3 1/5 Great Marlow School Mathematics Department