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May 6th, 2014, 09:43 AM   #1
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From: sutton coldfield

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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)
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May 6th, 2014, 09:44 AM   #2
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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.
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May 6th, 2014, 10:47 AM   #3
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Quote:
Originally Posted by fliss1992 View Post
Evaluate the following (find x)

x + 4 = 17

x - 4 = -2

14 = 2x

8x + 9 = 33

x^2 = 25
$\displaystyle x + 4 = 17$
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.
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May 6th, 2014, 10:49 AM   #4
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Quote:
Originally Posted by fliss1992 View Post
g ^ 3 divided by g =
$\displaystyle
\frac {g^3}{g} = \frac {g * g * g}{g} = g * g
$
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May 7th, 2014, 01:36 AM   #5
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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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