Question

How do you solve $2y + 3 = 5y - 6$?

Answer 1

Hint: In this question, we want to solve the linear equation of one variable. A linear equation of one variable can be written in the form $ax + b = c$. Here, a, b, and c are constants. And the exponent on the variable of the linear equation is always 1. To solve the linear equation, we have to remember that addition and subtraction are the inverse operations of each other. For example, if we have a number that is being added that we need to move to the other side of the equation, then we would subtract it from both sides of that equation.

Complete step by step solution:
In this question, we want to solve the linear equation of one variable.
The given equation is,
$ \Rightarrow 2y + 3 = 5y - 6$
Let us solve this equation,
First, we will subtract 5y on both sides.
That is equal to,
$ \Rightarrow 2y - 5y + 3 = 5y - 5y - 6$
Let us apply subtraction on both sides. The subtraction of 2y and 5y is equal to -3y on the left-hand side, and the subtraction of 5y and 5y is equal to 0 on the right-hand side.
Therefore,
$ \Rightarrow - 3y + 3 = - 6$
Now, let us subtract 3 on both sides.
$ \Rightarrow - 3y + 3 - 3 = - 6 - 3$
Let us apply subtraction on both sides. The subtraction of 3 and 3 is equal to 0 on the left-hand side, and the subtraction of -6 and 3 is equal to -9 on the right-hand side.
Therefore,
$ \Rightarrow - 3y = - 9$
Let us divide both sides by -3.
$ \Rightarrow \dfrac{{ - 3y}}{{ - 3}} = \dfrac{{ - 9}}{{ - 3}}$
That is equal to,
$ \Rightarrow y = 3$

Hence, the solution of the given equation is 3.

Note:
Let us verify the answer.
$ \Rightarrow 2y + 3 = 5y - 6$
Let us substitute the value of y as equal to 3 in the above equation.
$ \Rightarrow 2\left( 3 \right) + 3 = 5\left( 3 \right) - 6$
That is equal to,
$ \Rightarrow 6 + 3 = 15 - 6$
Let us simplify both sides.
$ \Rightarrow 9 = 9$
Hence, the answer we get is correct.