# How do you solve and write the following in interval notation: 2x - (7 + x) <= x?

Oct 4, 2016

$x \in \left(- \infty , \infty\right)$

#### Explanation:

$2 x - \left(7 + x\right) \le x$

$\implies 2 x - 7 - x \le x$

$\implies x - 7 \le x$

$\implies - 7 \le 0$

As the above is a tautology (always true, regardless of the value of $x$), the solution set is all real numbers. In interval notation, we can write this as having the endpoints of $\pm \infty$:

$x \in \left(- \infty , \infty\right)$