# Can you please show me how you solved the equation (x/6 + x/12 + x/7 + 5 + x/2 + 4 = x)

Brain Teasers
New answer on Apr 15, 2020
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Hi Cosma,

Here is one way (not saying it's the only one :)

First step: get all multiples of 2 to the same high denominator:

x/6 + x/12 + x/7 + 5 + x/2 + 4 = x <=> 2x/12 + x/12 + x/7 + 5 + 6x/12 + 4 = x

2x/12 + x/12 + x/7 + 5 + 6x/12 + 4 = x <=> 9x/12 + x/7 + 9 = x

And actually your equation is equivalent to 3x/4 + x/7 + 9 = x

Then you bring it all to the same denominator which gives you 21x/28 + 4x/28 + 9 = x

And finally you have 9 = 3x/28 which is equivalent to x = 28*3 = 84

Hope this helps :)

I would find the common denominator for ALL numbers together:

• 12= 2 x 2 x 3
• 6 > included in the 12
• 2 > included in the 12
• 7 = prime

Common denominator: 12 x 7

If you are more or less good with math you should have no issue, since it´s multiplications of one single digit.

Hope it helps!

Cheers,

Clara