Respuesta :
The solution set to inequality is:
[tex]\boxed{-1.5\left(4x+1\right)>4.5-2.5\left(x+1\right)\quad :\quad \begin{bmatrix}\mathrm{Solution:}\:&\:x<-1\:\\ \:\mathrm{Interval\:Notation:}&\:\left(-\infty \:,\:-1\right)\end{bmatrix}}[/tex]
Solution:
Given inequality is:
[tex]-1.5(4x + 1) > 4.5 -2.5(x + 1)[/tex]
We have to find the solution set to inequality
From given,
[tex]-1.5(4x + 1) > 4.5 -2.5(x + 1)\\\\\mathrm{Multiply\:both\:sides\:by\:}10\\\\-1.5\left(4x+1\right)\cdot \:10>4.5\cdot \:10-2.5\left(x+1\right)\cdot \:10\\\\-15\left(4x+1\right)>45-25\left(x+1\right)[/tex]
Expand
[tex]-60x -15 > 45 -25x - 25\\\\Simplify\\\\-60x-15>-25x +20[/tex]
[tex]\mathrm{Add\:}15\mathrm{\:to\:both\:sides}\\\\-60x-15+15>-25x+20+15\\\\Simplify\\\\-60x>-25x+35\\\\\mathrm{Add\:}25x\mathrm{\:to\:both\:sides}\\\\-60x+25x>-25x+35+25x\\\\Simplify\\\\-35x>35\\\\\mathrm{Multiply\:both\:sides\:by\:-1\:\left(reverse\:the\:inequality\right)}\\\\\left(-35x\right)\left(-1\right)<35\left(-1\right)\\\\\mathrm{Simplify}\\\\35x<-35\\\\\mathrm{Divide\:both\:sides\:by\:}35\\\\\frac{35x}{35}<\frac{-35}{35}\\\\\mathrm{Simplify}\\\\x < -1[/tex]
Thus the solution set is:
[tex]-1.5\left(4x+1\right)>4.5-2.5\left(x+1\right)\quad :\quad \begin{bmatrix}\mathrm{Solution:}\:&\:x<-1\:\\ \:\mathrm{Interval\:Notation:}&\:\left(-\infty \:,\:-1\right)\end{bmatrix}[/tex]
