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.