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Transcript
Algebra Equations Absorb mathematics: Solving equations ‘Look and See’ Each letter in an equation represents an ‘unknown’ number: unknown 3 (3) x + 1 = 10 Remember 3x means 3 × x It ain’t. x is 3 !! A little bit of trial and error might be required to find a value for x. I say X is 4 !! Replace the unknown with the number in brackets. ‘Look and See’ Each letter in an equation represents an ‘unknown’ number: 3 (3) x + 1 = 10 9 + 1 = 10 Both sides of the equal sign are the same. 10 = 10 No you didn’t! I told you x was 3! Class practice. Look at the following equations and solve by trial and error: 5 (8) x – 9 = 31 – 9would = 31 Hint:40 What you take 9 from to leave31 31?= 31 Class practice. Look at the following equations and solve by trial and error: Hint: You have to deal with the brackets first! 6 times what will give you 30? 6( (7) x – 2 ) = 30 6 (5) = 30 30 = 30 Balancing equations. A calculator might be required. At some point equations become too difficult to solve by eye. A method is required to find the unknown value. Balancing the equation This is where we treat each equation like a balanced set of scales. Look at the following equation: 4 + x== 77 Expressions Left Hand Side Right Hand Side Think of each equation as a balance. IT IS IMPORTANT TO CLEARLY SHOW ALL YOUR WORKING OUT! Example: Remember, the left hand side (LHS) is equal to the right hand side (RHS). LHS 3x+ RHS -1 -1 1 = 10 [ -1 each side] 3x=9 Take away 1 from both sides. A: The LHS must always equal the RHS. So whatever is done to one side must be done on the other side of the equal sign. Why both sides? IT IS IMPORTANT TO CLEARLY SHOW ALL YOUR WORKING OUT! Example: -1 Now divide both sides by 3. 3x ÷ 3 => 3x 3 =x 3 x + 1 = 10 ÷3 3x=9 X=3 -1 ÷3 [ -1 each side] [ ÷3 each side] Example: keyword 4( x + 2 ) = 20 The LHS is a product, 4 × brackets. Two choices for first step: Either a) ÷ 4 both sides. or b) multiply out brackets. Lets do b) ! Example: 4( x + 2 ) = 20 -8 -8 4x + 8 = 20 [- 8 each side] ÷4 ÷4 [÷ 4 each side] 4x = 12 x =3 Formulae. Look at the shape below: Find the value of x if the perimeter is 12 cm. Perimeter = 12 cm. X cm X cm 6 cm + + = 12 -6 -6 2x + 6 = 12 [-6 each side] ÷2 ÷2 2x = 12 [÷2 each side] x = 6 cm