Question

Solve the given linear equation $ y-9=21 $ for the value of y.

Answer 1

Hint: We will be using the concept of solving a linear equation in one variable. The equation means two expressions set equal to each other. Therefore, a linear equation can be written as $a\times x+b=c$ where a, b, c are constants.

Complete step-by-step solution -
We have to solve the equation y-9=21. We know that a solution is the value such that when replaced by the variable with it makes the equation true.
We will be solving it by using the general method of solving a linear equation. In the general method of solving linear equations, we use inverse operations.
Inverse operation means to get the variable for which you want to solve on one side and get everything else on the other side of the equation.
Now we can understand this inverse operation as follows: -
If a=b, then $a+c=b+c$
This means that if two expressions are equal, we can add the same thing on both sides.
If a=b, then $a-c=b-c$
This means that if two expressions are equal, we can subtract the exact two things on both sides.
Now we will use the inverse operation to solve the equation.
y-9=21
Now in this equation, we have to solve for variable y. So accordingly, we will use inverse operations so that y remains on one side of the equation and rest everything on the other side.
Now to do so we have to move -9 to the other side.
So, we can add the same number 9 on both sides so that it gets cancelled on the left side leaving y only on the left side.
y-9+9=21+9
y+0=30
y=30
Hence the value of y which solves the equation is 30.

Note: The solution can be simplified like if we keep a few things in mind like a number or variable is added on one side then on moving to the other side it gets subtract or its sign gets changed. For example, x+3=7 becomes x=7-3 here the sign of 3 gets changed from positive to negative on moving from left to right.