The solution to given inequality is: x < -1
Solution:
Given inequality is:
[tex]9-x>10[/tex]
We have to solve the inequality for "x"
Let us solve the inequality step by step
[tex]9-x>10\\\\\mathrm{Subtract\:}9\mathrm{\:from\:both\:sides}\\\\9-x-9>10-9\\\\\text{Simplify the above equation }\\\\-x>1\\\\\mathrm{Multiply\:both\:sides\:by\:-1\:\left(reverse\:the\:inequality\right)}[/tex]
The important rule in inequality is:
Whenever you multiply or divide an inequality by a negative number, you must flip the inequality sign.
[tex]\left(-x\right)\left(-1\right)<1\cdot \left(-1\right)\\\\\mathrm{Simplify}\\\\x<-1[/tex]
Thus the solution to given inequality is:
[tex]\boxed{9-x>10\quad :\quad \begin{bmatrix}\mathrm{Solution:}\:&\:x<-1\:\\ \:\mathrm{Interval\:Notation:}&\:\left(-\infty \:,\:-1\right)\end{bmatrix}}[/tex]
