Question

How do you make $t$ the subject of the formula \[2\left( {d - t} \right) = 4t + 7?\]

Answer 1

Hint: To make a variable the subject of the formula means to make that variable the dependent variable and others as independent one. In other words, simplifying the equation or the given formula in such a way that the subject should lie at the left hand side and other else at right hand side of the formula with help of algebraic operations.

Complete step by step solution:
In order to make $t$ the subject of the given formula, \[2\left( {d - t} \right) = 4t + 7\]
So we have to simplify the given formula such that $t$ should lie on the left hand side of the given equation, and other variables and constants on the right side of the equation and we will make it possible with the help of algebraic operations as follows
We have,
\[ \Rightarrow 2\left( {d - t} \right) = 4t + 7\]
Using distributive property of multiplication over subtraction to simplify the equation, we will get
\[ \Rightarrow 2d - 2t = 4t + 7\]
Now, subtracting $2d$ from both sides of the equation, we will get
\[
   \Rightarrow 2d - 2t - 2d = 4t + 7 - 2d \\
   \Rightarrow - 2t = 4t + 7 - 2d \\
 \]
Again subtracting $4t$ from both sides of the equation,
\[
   \Rightarrow - 2t - 4t = 4t + 7 - 2d - 4t \\
   \Rightarrow - 6t = 7 - 2d \\
 \]
Now, dividing both sides of the equation with coefficient of $t$ to get the required equation, in which $t$ will be the subject,
\[
   \Rightarrow \dfrac{{ - 6t}}{{ - 6}} = \dfrac{{7 - 2d}}{{ - 6}} \\
   \Rightarrow t = \dfrac{{2d - 7}}{6} \\
 \]
Therefore \[t = \dfrac{{2d - 7}}{6}\] is the required simplified form of the formula in which the subject is $t.$

Note: If we need to make some particular variable in formula as a subject it suggests that we have to resolve the formula for that variable, as we have done in this question. Also when applying the algebraic operation, then apply it to both sides of the equation in order to maintain the balance of the equation.