Question

How do you solve for x in \[16w + 4x = y\] ?

Answer 1

Hint: Here in this question, we have to solve the given algebraic equation for the x variable. The given equation has three variables x, y and w. To solve this equation for y by using arithmetic operation we can shift the variable w and its coefficient to the right hand side of the equation and on further simplification we get the required solution for the above equation.

Complete step by step solution:
The given equation is a algebraic equation with three variables
Consider the given equation
 \[16w + 4x = y\] .
Where, w, x and y are variables
16 is the coefficient of the w variable, 4 is the coefficient of x variable
Now, we need to solve the given equation for the x variable
 \[ \Rightarrow 16w + 4x = y\]
Subtract both side by 16w, then
 \[ \Rightarrow 16w + 4x - 16w = y - 16w\]
On simplification, we get
 \[ \Rightarrow 4x = y - 16w\]
For solve x, we keep only x variable In the left hand side of the equation.
Now divide the whole equation by 4 we have
 \[ \Rightarrow \dfrac{{4x}}{4} = \dfrac{{y - 16w}}{4}\]
On simplification, we get
 \[ \Rightarrow x = \dfrac{{y - 16w}}{4}\]
or
On rearranging this equation, we have
 \[ \Rightarrow x = \dfrac{y}{4} - \dfrac{{16w}}{4}\]
Again, by simplification
 \[ \Rightarrow x = \dfrac{y}{4} - 4w\]
Hence, the required solution is \[x = \dfrac{{y - 16w}}{4}\] or \[x = \dfrac{y}{4} - 4w\] .
So, the correct answer is “ \[x = \dfrac{{y - 16w}}{4}\] or \[x = \dfrac{y}{4} - 4w\] .”.

Note: The given equation is of the form of the algebraic equation. Here we have to find the equation for the variable x. If we want to write the equation for the variable, we transfer the other variable or terms or constants to the other side. While shifting or transferring the terms the sign will change. Hence we obtain the required result for the given question.