1. Solve x-5<10x-23

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

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