Inequality

**ashleydevos** · January 14th 2010, 05:23 PM

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?

**skeeter** · January 14th 2010, 05:35 PM

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 $x$

**Bacterius** · January 14th 2010, 05:36 PM

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

$2x - 7 - x \leq x$

$x - 7 \leq x$

$-7 \leq 0$

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

EDIT : erf Skeeter beat me to it

**ashleydevos** · January 14th 2010, 07:01 PM

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

**Bacterius** · January 14th 2010, 07:20 PM

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 : $x = (-\infty, +\infty)$ , $x \in \mathbb{R}$ .

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