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Question: How do you solve for ‘a’ in \[x = - \dfrac{b}{2}a\]?...

How do you solve for ‘a’ in x=−b2ax = - \dfrac{b}{2}a?

Explanation

Solution

Given equation is a simple question. We need to solve for ‘a’ in the above equation. First we multiply the whole equation by 2. After that we divide the whole equation by ‘b’ we will get the required answer. We can solve this using the transpose method.

Complete step by step solution:
Given, ⇒x=−b2a \Rightarrow x = - \dfrac{b}{2}a,

Since we can see that we have ‘2’ on the right hand side of the equation. We can transpose it to the
left hand side of the equation by multiplying on both sides with ‘2’. That is we,
⇒2.x=−b.a\Rightarrow 2.x = - b.a

Since we have ‘b’ on the right side of the equation. We transpose ‘b’ on the left side of the equation
by dividing ‘b’ on the both side we have,
⇒2xb=−a\Rightarrow \dfrac{{2x}}{b} = - a

Rearranging we have,
⇒−a=2xb\Rightarrow - a = \dfrac{{2x}}{b}

Multiplying negative sign on both side we get,
⇒a=−2xb\Rightarrow a = - \dfrac{{2x}}{b}.

Note: We can also solve the given problem in terms of ‘b’. we have, x=−b2ax = - \dfrac{b}{2}a. Since we have ‘a’ on the right side of the equation. We transpose ‘a’ on the left side of the equation by dividing ‘a’ on both sides and also we have ‘2’ on the right hand side of the equation. We can
transpose it to the left hand side of the equation by multiplying on both sides with ‘2’. We have,
⇒2xa=−b\Rightarrow \dfrac{{2x}}{a} = - b

Rearranging the equation and multiplying by negative sign on both side of the equation we have,
⇒b=−2xa\Rightarrow b = - \dfrac{{2x}}{a}. Since we have three variables (unknown values) in the given
equation we can find the other if we know the value of two variables.