May 6th, 2014, 09:43 AM  #1 
Newbie Joined: May 2014 From: sutton coldfield Posts: 11 Thanks: 0  Expressions
Hi  g ^ 3 divided by g = I have to simplify this expression, but I'm stuck on doing so. I did this one before, h^2 + h^2 = h^2 (two lots of the same term) 
May 6th, 2014, 09:44 AM  #2 
Newbie Joined: May 2014 From: sutton coldfield Posts: 11 Thanks: 0 
Evaluate the following (find x) x + 4 = 17 x  4 = 2 14 = 2x 8x + 9 = 33 x^2 = 25 I just need to be shown how to work it out, from then I should be able to work out the answer. 
May 6th, 2014, 10:47 AM  #3  
Senior Member Joined: Mar 2012 From: Belgium Posts: 653 Thanks: 11  Quote:
subtract 4 from both sides: $\displaystyle x + 4  4 = 17  4$ $\displaystyle x = 13$ $\displaystyle 14 = 2x$ divide both sides by 2: $\displaystyle \frac {14}{2}=\frac {2x}{2}$ $\displaystyle 7=x$ I hope this gives you enough to solve the rest too.  
May 6th, 2014, 10:49 AM  #4 
Senior Member Joined: Mar 2012 From: Belgium Posts: 653 Thanks: 11  
May 7th, 2014, 01:36 AM  #5 
Senior Member Joined: Apr 2014 From: Glasgow Posts: 2,068 Thanks: 692 Math Focus: Physics, mathematical modelling, numerical and computational solutions 
This is what I used to teach my students: i) if you have an equation (= sign) then you must do stuff to both sides to keep it balanced. ii) imagine you are an x... what happens to you? then try the opposite. The first point is easy to justify. The equals sign (=) really does mean that one side has to be exactly equal to the other side, so if you imbalance it by changing one side, you have to change the whole other side in the same way. So if I decide to multiply one side by 3, I have to multiply the other side by 3 too to keep it balanced. The second point is more of a tip for the simpler problems and doesn't always work, but it can help figure out what to do, especially when there is only one letter. Let's take the fourth question you put up: $\displaystyle 8x + 9 = 33$ If you imagine you are the x, what happens to you? Well, two things happen and they happen in this order first: multiply by 8 second: add 9 That happens and we end up with 33. We want to do the opposite of that and in reverse order. So basically we want to first: subtract 9 (the opposite of add 9) second: divide by 8 (the opposite of multiply by Let's actually do it: $\displaystyle 8x + 9 = 33$  subtract 9: $\displaystyle 8x + 9  9 = 33  9$ $\displaystyle 8x = 24$  divide by 8: $\displaystyle \frac{8x}{8} = \frac{24}{8}$ $\displaystyle x = 3$ Like I said though, this is only for some of the easy stuff at the beginning of the course. Hopefully, with a lot of practise, you'll get a feel for when this technique works and when it doesn't work. 

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