Question

Solve the equation x-15=0

Answer 1

- Hint: In this question we can use the 2nd axiom of Euclid which states that
‘If equals are added to equals, the holes (sums) are equal.’
Now, this can be explained with an example as follows
Let us say
2+3-1=4
Now, if we add 1 to both the sides, we will get
\[\begin{align}
  & \Rightarrow L.H.S.=2+3-1+1 \\
 & \Rightarrow L.H.S.=2+3=5 \\
\end{align}\]
Now, for R.H.S., we will get
\[\begin{align}
  & \Rightarrow R.H.S.=4+1 \\
 & \Rightarrow R.H.S.=5 \\
\end{align}\]
As L.H.S. and R.H.S are equal, hence, we can show the proof of the axiom.

Complete step-by-step solution -

As mentioned in the question, we have to find the value of x in the equation that is given to us.
We have to solve and the value of x in the following equation
x-15=0
Now, on using the 2nd axiom of Euclid, we can say that
If equals (that is 15 in this case) is added to equals, then wholes (sums) are equal which means the L.H.S. and the R.H.S are equal. So, we can write as follows
\[\begin{align}
  & x-15=0 \\
 & \Rightarrow L.H.S.=x-15 \\
 & \Rightarrow L.H.S.=x-15+15 \\
 & \Rightarrow L.H.S.=x \\
 & \\
 & \Rightarrow R.H.S.=0 \\
 & \Rightarrow R.H.S.=0+15 \\
 & \Rightarrow R.H.S.=15 \\
\end{align}\]
Now, as L.H.S and R.H.S are equal, hence, we get the equation as follows
x=15
So, we get the value of x as 15.

Note:- It is important to know the basic axioms of Euclid as they can become very useful in certain situations.
Also, we could have done this question by another method which is as follow
We can simply just transpose the 15 that is on the left hand side and get it over to the right hand side.
Hence, we can also get the same result.