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Solve the following inequality and enter your answer as an interval

Solve the following inequality and enter your answer as an interval-example-1
User ChrisShick
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1 Answer

4 votes

Given the following inequality:


(9)/(2)+x<(22)/(18)

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


\begin{gathered} (9)/(2)+x-(9)/(2)<(22)/(18)-(9)/(2) \\ \\ x<(22)/(18)-(9)/(2) \\ x<-(59)/(18) \end{gathered}

The answer as interval notation will be as follows:


(-\infty,-(59)/(18))

Another method to solve the inequality :


(9)/(2)+x<(22)/(18)

Multiplying both sides by 18:


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

User Matt Hidinger
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