Question 689237
{{{(3/7)*x=24}}}

to solve this equation means to get an answer for x. So we want to get the equation in the form x=SOMETHING. So we try to get x alone on one side by doing the following:
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Step 1: Multiply both sides of the equation by 7 
 
{{{(3/7)*(7)*x=24*(7)}}}

why does this cancel the 7 on the left?
{{{(3/7)*(7/1)}}}
{{{((3*7)/(7*1))}}}
{{{((3*7)/(1*7))}}}
{{{((3/1)*(7/7))}}} 

Anything divided by 1 equals itself (if there are 5 pencils and there is one person there are 5 pencils per person 5/1=5) so 3/1=3

Anything divided by itself equals 1 (if there are 5 pencils and there are 5 people there is 1 pencil per person 5/5 =1) so 7/7=1

Now the equation is

{{{3*x=24*(7)}}}
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step 3: divide by 3 on both sides

{{{(3*x)/3=(24*7)/3}}}
{{{(3/3)*x=(24*7)/3}}}
{{{x=(24*7)/3}}}

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step 4: simplify the left by factoring 

24 is the same as 2*(12) same as 2*2*(6) same as 2*2*2*3 now we put this in for 24

{{{x=((2*2*2*3)*7)/3}}}
{{{x=((2*2*2*7)*3)/3}}}
{{{x=(2*2*2*7)*(3/3)}}}
{{{x=(2*2*2*7)}}}
{{{x=(2*2*14)}}}
{{{x=(2*28)}}}
{{{x=(56)}}}