Question

How do you solve for z in \[a = x + y + \dfrac{z}{3}\]?

Answer 1

Hint: Here in this question, we have to solve the given equation to the z variable. The given equation is the algebraic equation with three variable x, y and z this can be solve by add or subtract the necessary term from each side of the equation to isolate the term with the variable z, then multiply or divide each side of the equation by the appropriate value, while keeping the equation balanced then solve the resultant balance equation for the z value.

Complete step-by-step answer:
In mathematics we have an algebraic equation where the algebraic equation is a combination of variables and constants.
Consider the given equation
\[a = x + y + \dfrac{z}{3}\]--------(1)
Now, we have to solve the above equation for the variable z
Multiply both sides of the equation (1) by 3
\[ \Rightarrow \,\,3a = 3\left( {x + y + \dfrac{z}{3}} \right)\]
Multiply 3 in to each term in RHS
\[ \Rightarrow \,\,3a = 3x + 3y + z\]-------(2)
Subtract 3x and 3y on both side of equation (2) then
\[ \Rightarrow 3a - 3x - 3y = 3x + 3y + z - 3x - 3y\]
On simplification, we get
\[ \Rightarrow 3a - 3x - 3y = z\]
On rearranging, the above equation can be written as
\[ \Rightarrow z = 3a - 3x - 3y\]
3 as common in each term on RHS, take it as common or Factor out the 3 in RHS, then
\[ \Rightarrow z = 3\left( {a - x - y} \right)\]
Hence, the required solution is \[z = 3\left( {a - x - y} \right)\].
So, the correct answer is “\[z = 3\left( {a - x - y} \right)\]”.

Note: In this question we solve the given equation for the one variable. While shifting the terms we must take care of signs. When the term is moving from one side to another side the sign will change. The term is in the form of fraction so we use the LCM procedure and we obtain the solution for the question.