Question

How do you solve for a in $sa = 2ab + 2ac + 2bc?$

Answer 1

Hint: Here we will move all the terms on the opposite side and will make the required term “a” the subject and then will simplify for the resultant required value.

Complete step-by-step solution:
Take the given expression: $sa = 2ab + 2ac + 2bc$
Move the term without “a” on the left hand side of the equation from the right hand side of the equation. When you move any term from one side of the equation to the opposite side, then the sign of the term also changes. Positive terms become negative and vice-versa.
$\Rightarrow sa - 2bc = 2ab + 2ac$
Now take out the common multiple common on the right hand side of the above equation.
$\Rightarrow sa - 2bc = 2a(b + c)$
The above expression can be re-written as –
$\Rightarrow 2a(b + c) = sa - 2bc$
Term multiplicative on one side if moved to the opposite side then it goes to the denominator.
$\Rightarrow a = \dfrac{{sa - 2bc}}{{2(b + c)}}$
This is the required solution.

Thus the required answer is $a = \dfrac{{sa - 2bc}}{{2(b + c)}}$

Note: Always remember that when you move any term from one side of the equation to the opposite side then the sign of the terms also changed. Positive term changes to negative term and the negative term changes to the positive term. When any solution is asked for any specific term, make it the subject moving all the other terms on the opposite side of the equation resulting in the required solution.