Question

How do you solve \[12y=2y+40\]?

Answer 1

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

Complete step-by-step solution:
We are given the equation \[12y=2y+40\], we have to solve it. The highest power of the variable of the equation is 1, so the degree of the equation is also one. Hence, it is a linear equation. As we know to solve a linear equation, we have to take all the variable terms to one side of the equation and leave constants to the other side.
\[12y=2y+40\]
Subtracting \[2y\]from both sides of the above equation, we get
\[\Rightarrow 10y=40\]
Dividing both sides by 10, we get
\[\Rightarrow \dfrac{10y}{10}=\dfrac{40}{10}\]
Canceling out common factor from numerator and denominator on both sides of the above equation, we get
\[\therefore y=4\]
Hence, the solution of the given equation is \[y=4\].

Note: We can check if the solution is correct or not by substituting the value we got in the equation. For the given equation, the left-hand side is \[12y\], and the right-hand side is \[2y+40\]. Substituting \[y=4\] in both sides of the above equation, we get \[LHS=12(4)=48\], and \[RHS=2(4)+40=48\]. As \[LHS=RHS\] the solution is correct.