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.