Changes

Now we compare the value given in the equation to the value we find found (above) for x.

<p style="text-align:center;"> {{highlight|Without fail, 2(1+2) will always equal (2*1 + 2*2), this is the '''Distributive Law.'''}}</p>

In the majority of incorrect proofs the respondent will cite PEMDAS or BODMAS, we all agree that parentheses or brackets are processed first. However, these solvers some respondents incorrectly resolve the [P]arenthesis arentheses or [B]rackets of PEMDAS - BODMAS. For , for some reason, these solvers believe that they can resolve within the parentheses, but ignore neglect to multiply the adjacent and dependent coefficient.

Then in In the division step, we must apply division to the (entire) implicitly connected termparenthetical expression. We cannot apply division to the coefficient (2) and then not apply division to the factor (2+1).

'''Incorrect:''' (''because division is not EXPLICITLY applied to (1+2) the entire parenthetical expression'')<div style="color:red;"><div style="width:200px60px; text-align:center; float:left; color:red;">::6 :--------- * (1+2) </div><div style="width:60px; text-align:center; float:2 left;"><br/><nowiki>*</nowiki><br/>

<div style="color:green;"><div style="width:200px60px; text-align:center; float:left; color:green;">6 ---- 1 </div><div style="width:60px; text-align:6 &nbspcenter;&nbspfloat:left;&nbsp"><br/>÷<br/></div> <div style="width:60px;&nbsptext-align:center;&nbsp;&nbsp;&nbsp;&nbspfloat:left;">2(1+2) :--------- ÷ ---------1 </div> <div style="width:60px; text-align:2 &nbspcenter;&nbspfloat:left;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 1"><br/>=<br/>

'''Correct:''' (''For multiplication, inverting the denominator will maintain its value.'') <div style="width:200px60px; text-align:center; float:left; color:green;">::6 &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 2 * (1+2) :--------- 6 * ---------1 </div>::2 &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; (1+2)</div>

'''SolutionTraditional solution:'''

<div style="width:100px60px; text-align:center; float:left;">

<div style="width:100px60px; text-align:center; float:left;">

<div style="width:100px60px; text-align:center; float:left;">

1*(1+2)

<div style="width:100px60px; text-align:center; float:left;">

<div style="width:100px60px; text-align:center; float:left;">

<div style="width:100px60px; text-align:center; float:left;">

When we reduce by the common divisor, this does not complete the division operation, it simply reduces the coefficient to one. Division must be applied to both the factor and the coefficientof the parenthetical expression. 

We would not write 2(a+b) as (2(a+b)), nor can we re-write the given equation as 6÷2*(a+b) and maintain the same value. We can however, rewrite the full equation to include an explicit multiplier if we take care to maintain the grouping parenthetical expression with additional bracketing 6÷(2*(a+b)).

Entering the equation into a programming language, or low quality calculator, requires the explicit multiplication symbol and outer parenthesis to maintain value of the groupingparenthetical expression.