Question

Solve the following inequality.

-2/3x>8
A) x < - 4



B) x > - 4



C) x > -12



D) x < -12

Answer 1

First simplify.

`-(2)/(3)x \ \textgreater \ \mathrm{Multiply\:fractions}:\ \:a\cdot (b)/(c)=(a\:\cdot \:b)/(c) \ \textgreater \ -(2x)/(3)`


`\mathrm{Multiply\:both\:sides\:by\:-1\:\left(reverse\:the\:inequality\right)} \ \textgreater \ \ \textgreater \ (2x)/(3)\ \textless \ -8`


`\mathrm{Multiply\:both\:sides\:by\:}3 \ \textgreater \ (3\cdot \:2x)/(3)\ \textless \ 3\left(-8\right) \ \textgreater \ Simplify \ \textgreater \ 2x\ \textless \ -24`


`\mathrm{Divide\:both\:sides\:by\:}2 \ \textgreater \ (2x)/(2)\ \textless \ (-24)/(2) \ \textgreater \ Simplify \ \textgreater \ x\ \textless \ -12`


`Therefore\; x\ \textless \ -12 \;is\;our\;answer!`

Hope this helps!