Respuesta :
[tex]-38d-57>-19d+76\quad :\quad \begin{bmatrix}\mathrm{Solution:}\:&\:d<-7\:\\ \:\mathrm{Interval\:Notation:}&\:\left(-\infty \:,\:-7\right)\end{bmatrix}[/tex]
Solution:
Given inequality is:
[tex]-38d - 57 > -19d + 76[/tex]
We have to solve the inequality for "d"
From given,
[tex]-38d-57>-19d+76\\\\\mathrm{Add\:}57\mathrm{\:to\:both\:sides}\\\\-38d-57+57>-19d+76+57\\\\\mathrm{Simplify}\\\\-38d>-19d+133\\\\\mathrm{Add\:}19d\mathrm{\:to\:both\:sides}\\\\-38d+19d>-19d+133+19d\\\\[/tex]
[tex]\mathrm{Simplify}\\\\-19d>133\\\\Multiply\:both\:sides\:by\:-1\:\left(reverse\:the\:inequality\right)\\\\[/tex]
When we multiply or divide both sides of inequality by negative number, then we must flip the inequality sign
[tex]\left(-19d\right)\left(-1\right)<133\left(-1\right)\\\\\mathrm{Simplify}\\\\19d<-133\\\\\mathrm{Divide\:both\:sides\:by\:}19\\\\\frac{19d}{19}<\frac{-133}{19}\\\\\mathrm{Simplify}\\\\d<-7[/tex]
The solution set is given as:
[tex]-38d-57>-19d+76\quad :\quad \begin{bmatrix}\mathrm{Solution:}\:&\:d<-7\:\\ \:\mathrm{Interval\:Notation:}&\:\left(-\infty \:,\:-7\right)\end{bmatrix}[/tex]
