Question

How do you solve $\dfrac{3t}{2}+7=4t-3$?

Answer 1

Hint: To solve the given equation first we will solve the fraction given in the equation. Then by solving the algebraic operations like addition, multiplication and subtraction we get the desired answer. So, start by multiplying the whole equation with 2 and then proceed by shifting the variables and constants to either side of the equation.

Complete step-by-step solution:
We have been given an equation $\dfrac{3t}{2}+7=4t-3$.
We have to solve the given equation.
A linear equation in one variable has one variable and has only one solution. So by solving the equation we have to find the value of unknown variable. To solve the given equation first multiply the given equation by 2. Then we will get
$\Rightarrow \dfrac{3t}{2}\times 2+7\times 2=4t\times 2-3\times 2$
Simplifying the above obtained equation we will get
$\Rightarrow 3t+14=8t-6$
Now, shifting the constant terms to the right side and shifting the variable terms to the left side we will get
$\Rightarrow 3t-8t=-6-14$
Simplifying the above obtained equation we will get
$\Rightarrow -5t=-20$
Now, divide the equation by 5 we will get
$\Rightarrow \dfrac{-5t}{5}=\dfrac{-20}{5}$
Now, simplifying the above obtained equation we will get
$\begin{align}
  & \Rightarrow -t=-4 \\
 & \Rightarrow t=4 \\
\end{align}$
Hence on solving the given equation we get the value of t as 4.

Note: When there are a number of operations given in the equation we have to follow the BODMAS rule. According to this rule first we have to solve the brackets, then orders (power), then division, then multiplication and then addition or subtraction. BODMAS rule is used to explain the order of operation of mathematical expression.