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Cay1234 · Jun 13, 2009, 03:30 AM

1. Solve x-5<10x-23

2. Simplify (4x^3y^2)^-3 using positive indicies

Perito · Jun 13, 2009, 04:43 AM

x-5<10x-23
Simplify (4x^3y^2)^-3 using positive indicies

#1: You solve just as if it were a normal equation -- almost.

$x-5 < 10x-23$

$x-5-x+23 < 10x-x-23+23$

$18 < 9x$

In this case, there's no multiplying or dividing. If you multiply or divide by a negative number the sense of the equation will (from < to > or vice-versa). If, for example, you have an equation:

$9 > 3$

and you multiply both sides by -1, the "sense" of the inequality changes. If you multiply or divide by an unknown, you have to keep that in mind if the value comes out to be negative.

$-9 < -3$

#2.
$(4x^3y^2)^{-3}=\frac {1}{(4x^3y^2)^3}= \frac {1}{64 x^9 y^6}$