Is there any rules to be followed with the sign like switch the sign if it is negative?

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- Dec 29th 2008, 03:21 PMRussianAbsolute Inequalities
Is there any rules to be followed with the sign like switch the sign if it is negative?

- Dec 29th 2008, 04:35 PMShyam
INEQUALITY:

If you have,

$\displaystyle -2x \le 4$

then, the sign of inequality is switched if you multiply or divide both sides with a negative number (here, we divide both sides by -2)

$\displaystyle x\ge -2$

ABSOLUTE INEQUALITY:

If you have

$\displaystyle |x|\le 6$

then

$\displaystyle x \le 6$ and $\displaystyle x \ge -6$

If you have

$\displaystyle |2x|\ge 10$

then

$\displaystyle 2x \ge 10$ and $\displaystyle 2x \le -10$

$\displaystyle x \ge 5$ and $\displaystyle x \le -5$

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