Question

Solve the following inequality and enter your answer as an interval

Answer 1

Given the following inequality:

$\frac{9}{2}+x<\frac{22}{18}$

We will solve the inequality as follows, subtract (9/2) from both sides

$\begin{gathered} \frac{9}{2}+x-\frac{9}{2}<\frac{22}{18}-\frac{9}{2} \\ \\ x<\frac{22}{18}-\frac{9}{2} \\ x<-\frac{59}{18} \end{gathered}$

The answer as interval notation will be as follows:

$(-\infty,-\frac{59}{18})$

Another method to solve the inequality :

$\frac{9}{2}+x<\frac{22}{18}$

Multiplying both sides by 18:

$\begin{gathered} 18\cdot(\frac{9}{2}+x)<18\cdot\frac{22}{18} \\ 18\cdot\frac{9}{2}+18x<22 \\ 81+18x<22 \\ 18x<22-81 \\ 18x<-59 \\ \\ x<-\frac{59}{18} \end{gathered}$