Prove that for all real numbers x, if 2x+1 is rational then x is rational

Answer with explanation:

It is given that,  for all real numbers x, if 2 x+1 is rational .

      When you will look at the expression ,2 x +1

⇒1 is rational

⇒2 x will be rational, because the expression , 2 x+1, is rational.

⇒2 x is rational, it means , x will be rational,because 2 is rational.

Some important rules considering rational and irrational

1.⇒Product of rational and rational is Rational.

2.⇒Product of Irrational and Rational is Irrational.

3.⇒Product of Irrational and Irrational may be irrational or rational.

≡2 x →is rational, 2 is rational number ,so x will be rational also.