Question

How do you solve \[\dfrac{x-3}{4}=\dfrac{7}{8}\]?

Answer 1

Hint:
 The above question is a simple problem of linear equations in one variable. So, we will simply first understand the concept and definition of linear equation in one variable and then we will solve the above question to get the value of ‘x’. We will first cross multiply the given fractions and then shift all constant terms at the RHS and all the variable terms at the LHS. Then we will simplify the obtained equation by using the basic algebraic operations. Then we will get the value of x.

Complete step by step answer:
We know that the linear equation in one variable is an equation that has a maximum of one variable in the equation which is of order 1. Also, we know that a linear equation in one variable has only one solution.
And, also the standard form of linear equation in one variable is represented as:
ax + b = 0 where a, b is real number and a is not equal to zero.
So, we can say that \[\dfrac{x-3}{4}=\dfrac{7}{8}\] is a linear equation in one variable with variable x.
First, we will use the cross-multiplication method to get a simpler form of the above equation.
So, after applying cross-multiplication method we will get:
\[\begin{align}
  & \Rightarrow \dfrac{x-3}{4}=\dfrac{7}{8} \\
 & \Rightarrow 8\left( x-3 \right)=4\times 7 \\
\end{align}\]
Now, we will open the parenthesis at the LHS, then we will get:
\[\begin{align}
  & \Rightarrow 8\left( x-3 \right)=4\times 7 \\
 & \Rightarrow 8\times x-8\times 3=28 \\
\end{align}\]
Now, performing the multiplication and simplifying further we will get:
\[\Rightarrow 8x-24=28\]
Now, to solve \[8x-24=28\] we will shift variable on one side of the equation from other side of the equation and similarly, we will shift constant on the same side of the equation.
\[\Rightarrow 8x=24+28\]
\[\Rightarrow 8x=52\]
So, after dividing both side by 8 we will get:
\[\begin{align}
  & \Rightarrow \dfrac{8x}{8}=\dfrac{52}{8} \\
 & \Rightarrow x=\dfrac{13}{2} \\
\end{align}\]
Now, when we will put \[x=\dfrac{13}{2}\] in the equation given above, then we will get $ \dfrac{7}{8}=\dfrac{7}{8} $ , which satisfies the equality.
Hence, \[x=\dfrac{13}{2}\] is our required answer.

Note:
 Students is required to recall the linear equations and basic properties of linear equations to solve these types of question. We can verify the answer by putting the value in the given equation. On solving the equation if we get the values of LHS and RHS equal it means that the answer is correct. Students are also required to note that when we shift variable or constant from one side of the equation to the other side of the equation then the sign of the variable gets reversed and the magnitude remains the same.