Question

How do you solve \[-1=\dfrac{5+x}{6}\]?

Answer 1

Hint: To solve an equation we have to find the value of the variable that satisfies the equation. The degree of the equation is the highest power to which the variable is raised. If the degree of the equation is 1, then the equation is linear. To solve a linear equation in one variable, we have to take the variable terms to one side of the equation, and the constants to the other side. By this, we can find the value of the variable.

Complete step-by-step solution:
The given equation is \[-1=\dfrac{5+x}{6}\]. Multiplying both sides of the equation by 6, we get
\[\Rightarrow -1\times 6=\dfrac{5+x}{6}\times 6\]
Canceling out 6 as a common factor of numerator and denominator in RHS, we get
\[\Rightarrow -6=5+x\]
The degree of the above equation is 1, hence it is a linear equation. We know that to solve a linear equation, we have to take the variable terms to one side, and constants to another side of the equation. We will do the same for the above equation.
\[\Rightarrow -6=5+x\]
Flipping the above equation, we get
\[\Rightarrow 5+x=-6\]
Subtracting 5 from both sides of the above equation, we get
\[\begin{align}
  & \Rightarrow 5+x-5=-6-5 \\
 & \therefore x=-11 \\
\end{align}\]
Hence, the solution of the equation \[-1=\dfrac{5+x}{6}\] is \[x=-11\].

Note: We can check whether the solution is correct or not by substituting the value of x in the given equation. By doing this we get
The LHS of the equation is \[-1\].
Substituting the value of x in the RHS of the equation, we get
\[\Rightarrow \dfrac{5+(-11)}{6}=\dfrac{5-11}{6}=\dfrac{-6}{6}\]
\[\Rightarrow -1\]
Hence, as the LHS of the equation equals the RHS, the solution is correct.