Question

Two step inequality 9-x>10

Answer 1

The solution to given inequality is: x < -1

Solution:

Given inequality is:

`9-x>10`

We have to solve the inequality for "x"

Let us solve the inequality step by step

`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)}`

The important rule in inequality is:

Whenever you multiply or divide an inequality by a negative number, you must flip the inequality sign.

`\left(-x\right)\left(-1\right)<1\cdot \left(-1\right)\\\\\mathrm{Simplify}\\\\x<-1`

Thus the solution to given inequality is:

`\boxed{9-x>10\quad :\quad \begin{bmatrix}\mathrm{Solution:}\:&\:x<-1\:\\ \:\mathrm{Interval\:Notation:}&\:\left(-\infty \:,\:-1\right)\end{bmatrix}}`