Solution:
Given inequality is:
[tex]-7d + 8> 29[/tex]
We have to solve the inequality
From given,
[tex]-7d + 8> 29[/tex]
[tex]\mathrm{Subtract\:}8\mathrm{\:from\:both\:sides}\\\\-7d+8-8>29-8\\\\\mathrm{Simplify}\\\\-7d>21\\\\\mathrm{Multiply\:both\:sides\:by\:-1\:\left(reverse\:the\:inequality\right)}[/tex]
When we multiply or divide the both sides of inequality by negative number, we have to flip the inequality sign
[tex]\left(-7d\right)\left(-1\right)<21\left(-1\right)\\\\\mathrm{Simplify}\\\\7d<-21\\\\\mathrm{Divide\:both\:sides\:by\:}7\\\\\frac{7d}{7}<\frac{-21}{7}\\\\d<-3[/tex]
Therefore,
[tex]-7d+8>29\quad :\quad \begin{bmatrix}\mathrm{Solution:}\:&\:d<-3\:\\ \:\mathrm{Interval\:Notation:}&\:\left(-\infty \:,\:-3\right)\end{bmatrix}[/tex]
