Question

How do you solve for x- \[\dfrac{x}{3}-15=12+x\]?

Answer 1

Hint: In this given problem we have to solve and get the value of x for the given linear equation. Solving for x is nothing but we have to find the value for x. We just have to cross multiply the left-hand side terms and after cross multiplying, the denominator we get should be shifted to the numerator of the right-hand side and multiply with the other terms to get the value of x.

Complete Step by step answer:
We know that the given linear equation is,
\[\dfrac{x}{3}-15=12+x\]
Now we can cross multiply the left-hand side in the above linear equation, we get
\[\begin{align}
  & \Rightarrow \dfrac{x-3\times 15}{3}=12+x \\
 & \Rightarrow x-3\times 15=3\left( 12+x \right) \\
\end{align}\]
 Here, we have shifted the denominator from the left-hand side to the right-hand side to be multiplied with the other terms, after multiplying, we get
\[\Rightarrow x-45=36+3x\]
Now, we can bring similar terms to the same side, we get
\[\begin{align}
  & \Rightarrow 3x-x=-45-36 \\
 & \Rightarrow 2x=-81 \\
\end{align}\]
Now we can divide by 2 on both sides and cancel similar terms, we get the value of x.
\[\begin{align}
  & \Rightarrow \dfrac{2x}{2}=\dfrac{-81}{2} \\
 & \Rightarrow x=\dfrac{-81}{2} \\
\end{align}\]
Therefore, the value of x is \[\dfrac{-81}{2}\]

Note:
Students make mistakes in shifting the sign, when shifting the positive sign to the other side it changes to negative and when shifting the negative sign to the other side it gets converted into positive and also students make mistakes after cross multiplying, the whole term is divided by the denominator. Students should be clear of the multiplication tables for these types of problems.