Question

solve -5(3x+4)/2 < 6-3x

Answer 1

SOLUTION

Given the question in the image, the following are the solution steps to answer the question.

STEP 1: Write th given inequality expression

$-\frac{5}{2}\left(3x+4\right)<6-3x$

STEP 2: Simplify the given expression

$\begin{gathered} \mathrm{Multiply\:both\:sides\:by\:}2 \\ \frac{-5\left(3x+4\right)}{2}\cdot \:2<6\cdot \:2-3x\cdot \:2 \\ -5\left(3x+4\right)<12-6x \\ -15x-20<12-6x \\ \mathrm{Add\:}20\mathrm{\:to\:both\:sides} \\ -15x-20+20<12-6x+20 \\ -15x<-6x+32 \\ -9x<32 \\ \mathrm{Multiply\:both\:sides\:by\:-1\:\left(reverse\:the\:inequality\right)} \\ \left(-9x\right)\left(-1\right)>32\left(-1\right) \\ 9x>-32 \\ x>-\frac{32}{9} \end{gathered}$

Hence, the solution gives:

$x\gt-\frac{32}{9}$