Question

Find $m$ where $7m+\dfrac{19}{2}=13$.

Answer 1

Hint: We separate the variables and the constants of the equation $7m+\dfrac{19}{2}=13$. We apply the binary operation of addition and subtraction for both variables and constants. The solutions of the variables and the constants will be added at the end to get the final answer to equate with 0. Then we solve the linear equation to find the value of $m$.

Complete step by step answer:
The given equation $7m+\dfrac{19}{2}=13$ is a linear equation of \[m\]. we need to simplify the equation by solving the variables and the constants separately. All the terms in the equation of $7m+\dfrac{19}{2}=13$ are either variables of $m$ or a constant. We first separate the variables. We take the constants all together to solve it.
$7m+\dfrac{19}{2}=13 \\
\Rightarrow 7m=13-\dfrac{19}{2} \\ $
There are two such constants which are 13 and $\dfrac{19}{2}$.
Now we apply the binary operation of subtraction to get
$7m=13-\dfrac{19}{2}=\dfrac{7}{2}$.
The binary operation between them is addition which gives us
$7m=\dfrac{7}{2}$.
Now we divide both sides of the equation with 7 to get
\[7m=\dfrac{7}{2} \\
\Rightarrow \dfrac{7m}{7}=\dfrac{7}{2\times 7} \\
\therefore m=\dfrac{1}{2} \\ \]
Therefore, the final solution becomes \[m=\dfrac{1}{2}\].

Note: We can verify the result of the equation $7m+\dfrac{19}{2}=13$ by taking the value of as \[m=\dfrac{1}{2}\]. Therefore, the left-hand side of the equation $7m+\dfrac{19}{2}=13$ becomes
$7m+\dfrac{19}{2}=7\times \dfrac{1}{2}+\dfrac{19}{2} \\
\Rightarrow 7m+\dfrac{19}{2}=\dfrac{7}{2}+\dfrac{19}{2} \\
\Rightarrow 7m+\dfrac{19}{2}=\dfrac{26}{2} \\
\therefore 7m+\dfrac{19}{2}=13$
Thus, verified for the equation $7m+\dfrac{19}{2}=13$ the solution is \[m=\dfrac{1}{2}\].