Question

Find the solution of \[K = 4a + 9ab\] for “a”.

Answer 1

Hint: To solve for \[a\] means to have \[a\] in terms of the other variables and numbers. To solve such equations first the term which needs to be obtained should be at one side that is all the terms including \[a\] should be at one side of the equation. Then the value to be obtained has to be taken in common so that it can be found.

Complete step-by-step answer:
Here we need to solve for “a” so first it should be seen which terms in the equation contain \[a\] .
In this type of equation, having more than one variable is unknown, we have to specify for which variable we want the equation to be solved.
First we need to pull out the like factors that are to solve for \[a\] means to have \[a\] in terms of the other variables and numbers.
Therefore, taking out \[a\] as the common factor we have,
 \[
  4a + 9ab = K \\
  \Rightarrow a\left( {4 + 9b} \right) = K \;
 \]
Now we have the common factor outside which has to be obtained. So now we need to divide by the bracket so that \[a\] remains in the left hand side and the bracket terms go to the right hand side.
Hence, we have
 \[ \Rightarrow a = \dfrac{K}{{4 + 9b}}\]
So, the value of \[a\] is \[\dfrac{K}{{4 + 9b}}\] .
So, the correct answer is “ \[\dfrac{K}{{4 + 9b}}\] ”.

Note: To solve for any variable means having that variable in terms of other variables and numbers so that common factors can be taken and keep them into brackets. Now we have the common factor outside which has to be obtained. The bracket has to be divided so that the unknown variable remains in the left hand side and bracket terms go to the right hand side.