Question

Which of the following is an unchanging relation?

• A. $x+x=2x$, for all numbers $x$
• B. $(x+y)-y=2y$, for all numbers $x$, $y$
• C. $x+(x+1)=2x+3$, for all numbers $x$
• D. If $x$ and $y$ are any two numbers, then $2x+2y=2\left(x\right)+y$

Answer 1

The correct option is A $x+x=2x$, for all numbers $x$

• Multiplying two numbers separately by 2 and then adding them is same as multiplying the sum of two numbers by 2.

i.e., If $x$ and $y$ are any two numbers, then $2x+2y=2(x+y)$

• If we take any natural number and add the next natural number, or if we double the first number and add 1 to it, we get the same result.

i.e., If $x$ is any number, then $x+(x+1)=2x+1$

• If to one number we add and subtract the same number, then we get the first number as the result.

i.e., $(x+y)-y=x$, for all numbers $x$, $y$.

• Any number added to itself is double the number.

i.e., $x+x=2x$, for all numbers $x$.