Question 234760
Here's the problem restated: {{{19+x/2=4}}}

Step 1. Isolate the variable by it's self 

{{{19+x/2-19=4-19 }}}

on the left hand side the two "19"'s cancel becoming...

{{{x/2=4-19}}}

"4-19" equals "-15" so rewriting 

{{{x/2=-15}}}

Step 2. Reverse whatever process is being done to "x" if "x" is being multiplied, you divide, if it's being divided, you multiply. etc 

{{{x/2=-15}}}

multiply both sides by two 

{{{2(x/2)=2(-15)}}}

The left hand side with "x" is being divided by "2" and multiplied by "2" these effects cancel each other out. 

{{{x=2(-15)}}} 

multiply the right hand side

{{{x=-30}}} 

To check our answer we input the solution we concluded which was "-30" into the original problem which was {{{19+x/2=4}}} 

{{{19+(-30)/2=4}}}
{{{19+(-15)=4}}}
{{{19-15=4}}}
{{{4=4}}}

Since we arrived at a mathematical truth (that "4" is indeed "4") the solution we concluded is indeed correct. It's my wish that you will be able to understand any type of problem of this manner. Please let me know if you have any further questions regarding this problem or any other math problem that's a puzzler for you.