# Inequality

• Jan 14th 2010, 06:23 PM
ashleydevos
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?
• Jan 14th 2010, 06:35 PM
skeeter
Quote:

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 $x$
• Jan 14th 2010, 06:36 PM
Bacterius
$2x - (7 + x) \leq x$

$2x - 7 - x \leq x$

$x - 7 \leq x$

$-7 \leq 0$

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

EDIT : erf Skeeter beat me to it :D
• Jan 14th 2010, 08:01 PM
ashleydevos
How do you write it in interval notation then? [-7<= ∞)???
• Jan 14th 2010, 08:20 PM
Bacterius
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 : $x = (-\infty, +\infty)$, $x \in \mathbb{R}$.