# Thread: Inequality

1. ## Inequality

Help!! I need help finding x.
2x – (7 + x) < x

2x - 7 - x <= x
x - 7 <= x

The x cancels out, so is the answer that circle with the diagonal line through it?

2. Originally Posted by ashleydevos
Help!! I need help finding x.
2x – (7 + x) < x

2x - 7 - x <= x
x - 7 <= x

The x cancels out, so is the answer that circle with the diagonal line through it?
$x-7 \le x$

you did not finish, subtract $x$ from both sides ...

$-7 \le 0$

a true statement ... therefore the inequality is true for all $x$

3. $2x - (7 + x) \leq x$

$2x - 7 - x \leq x$

$x - 7 \leq x$

$-7 \leq 0$

So this equality holds for any $x$, because $-7$ is indeed smaller than $0$.

EDIT : erf Skeeter beat me to it

4. How do you write it in interval notation then? [-7<= ∞)???

5. No, no !

Regardless of the value of $x$, the inequality holds, so I guess you could write this $x = \mathbb{R}$, or :

$\forall x \in \mathbb{R}$, $2x - (7 + x) \leq x$

A less elegant but more direct way to write it could be : $x = (-\infty, +\infty)$, $x \in \mathbb{R}$.