Question

Find the value of m.
\[7m+\dfrac{19}{2}=13\]
\[\begin{align}
  & A.\text{ }0.54 \\
 & B.\text{ }0.5 \\
 & C.\text{ }0.32 \\
 & D.\text{ }0.7 \\
\end{align}\]

Answer 1

Hint: In this question, we are given an equation in terms of variable m and we have to solve this equation to find the value of m. We will use step methods for solving this sum. We will first remove the constant term from the left side where the variable is present by subtracting constant term from both sides and then we will divide the coefficient of variable on both sides to get the variable alone on the left side and its solution will be given by the right side. We will also use LCM for finding subtraction of fractional terms with integers.

Complete step by step answer:
We are given equation as \[7m+\dfrac{19}{2}=13\]
We want to find the value of m which means we have to remove all constant terms and coefficients of m from the left side of the equation. We will do it using the step method.
Firstly, let us remove the constant term $\dfrac{19}{2}$ from the left side. For this, subtracting $\dfrac{19}{2}$ from both sides, we get:
\[\begin{align}
  & 7m+\dfrac{19}{2}-\dfrac{19}{2}=13-\dfrac{19}{2} \\
 & \Rightarrow 7m=13-\dfrac{19}{2} \\
\end{align}\]
Using LCM on right hand side, we get:
\[\Rightarrow 13-\dfrac{19}{2}=\dfrac{26-19}{2}=\dfrac{7}{2}\]
Therefore, equation becomes \[\Rightarrow 7m=\dfrac{7}{2}\]
As we can see, we are still stuck with 7 as coefficient of m but we only need value of m, therefore, let us divide both sides by 7, so we get:
 \[\Rightarrow \dfrac{7m}{7}=\dfrac{7}{2\times 7}\]
Solving this we get:
\[\Rightarrow m=\dfrac{1}{2}\]
Since, the left hand side of the equation does not have any constant term or coefficient of variable m, therefore, we have found the value of m.
Hence, value of \[\Rightarrow m=\dfrac{1}{2}\]
Now, let us convert it into decimal as all of our options are in decimal numbers. Therefore, multiplying numerator and denominator by 5, we get:
\[\Rightarrow m=\dfrac{1\times 5}{2\times 5}=\dfrac{5}{10}\]
As we know, we can write $\dfrac{5}{10}$ as 0.5
Therefore, value of m = 0.5

So, the correct answer is “Option B”.

Note: Students should carefully perform subtraction between fraction and integers. They can solve this equation directly in the following way: \[7m+\dfrac{19}{2}=13\]
Take $\dfrac{19}{2}$ to the right hand side, as it is positive on the left hand side so it becomes negative on the right hand side.
\[7m=13-\dfrac{19}{2}\]
Solving by taking LCM we get:
\[7m=\dfrac{7}{2}\]
Now, taking 7 from left hand side to right hand side. As 7 is multiplied on the left hand side so it will be divided on the right hand side. So, we get \[\Rightarrow m=\dfrac{7}{2}\div 7=\dfrac{7}{2}\times \dfrac{1}{7}=\dfrac{1}{2}=0.5\]
Students can use this method for solving these equations as well.