Question

How can I solve this? \[\dfrac{k}{7}+3-2k=-3\]

Answer 1

Hint: In this problem we have to solve and find the value of k. We can first take the terms with k on one side and the remaining terms to the other side. Then we can simplify the terms in order to get the value of k. We will use cross multiplication to find the value of k.

Complete step by step answer:
We know that the given equation to be solved to find the value of k is,
\[\dfrac{k}{7}+3-2k=-3\]
We can first subtract the number 3 on both the left-hand side and the right-hand side of the equation, we get
\[\begin{align}
  & \Rightarrow \dfrac{k}{7}+3-2k-3=-3-3 \\
 & \Rightarrow \dfrac{k}{7}-2k=-6 \\
\end{align}\]
Now we can take cross-multiplication in the above step, we get
\[\begin{align}
  & \Rightarrow \dfrac{k}{7}-2k=-6 \\
 & \Rightarrow \dfrac{k-\left( 7 \right)2k}{7}=-6 \\
\end{align}\]
Now we can multiply the numerator, we get
\[\Rightarrow \dfrac{k-14k}{7}=-6\]
We can now multiply the number 7 on both the left-hand side and the right-hand side of the equation, we get
\[\Rightarrow 7\times \dfrac{k-14k}{7}=-6\times 7\]
Now we can cancel the similar terms and subtract the terms in the above step, we get
\[\begin{align}
  & \Rightarrow k-14k=-42 \\
 & \Rightarrow -13k=-42 \\
\end{align}\]
We can now divide by the number -13 on both the left-hand side and the right-hand side of the equation, we get
\[\Rightarrow k=\dfrac{42}{13}\]
Therefore, the value of k is \[\dfrac{42}{13}\].

Note:
Students make mistakes while simplifying, as we have done lots of simplification in the above steps. We should know that to simplify and to solve, we have to multiply/divide the similar number in order to cancel the terms to get the exact value. We should also know cross multiplication, to solve these types of problems.