Harder and non-linear Equations

  • You've had plenty of practice with linear equations so let's move a step forward and go for the harder ones.
  • Example
  • When you see something like this, there is no need to panic!
  • You have all the tools to solve this equation but it'll take slightly longer than the ones you have done already.

  • Just remember our 3 methods for solving a simple equation:
    1. Flowchart
    2. Balance
    3. Trial and Error
  • Now let's try solving the equation by using the flowchart method.
  • It's easier if you first consider the steps from x to that nasty expression before you work your way backwards.
x + 20 ÷ 2 +3 4
Now working our way back we have:
4 42 = 3 + (x + 20)/2 16-3= (x+20)/2 13× 2 = x+20 26-20 = x
  • So there we have it, x=6. You will have noticed that I've combined this with the balancing method by putting the = signs in.

  • Note that we cant use the marbles and boxes idea anymore because square rooting marbles just doesn't make sense but the balance method still works!
  • You get the idea so I think you're ready for a bit of exercise!
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