Question

Solve the inequality. Then use the drop down menu to select the correct symbols to indicate your answer in interval notation. If a number is not an integer then round it to the nearest hundredth. To indicate positive infinifty ( \infty ) type the three letters "inf". To indicate negative infinity(-\infty ) type "-inf" with no spaces between characters. |\frac{x-3}{5}|<2 AnswerAnswer,AnswerAnswer

Answer 1

(-7, 13)

Step-by-step explanation:
`\begin{gathered} \text{Given:} \\ |\frac{x\text{ - 3}}{5}|\text{ < 2} \end{gathered}`

This is an absolute functon inequality, so we would get two x values:

`\begin{gathered} |\frac{x\text{ - 3}}{5}|\text{ < 2 means:} \\ \frac{x\text{ - 3}}{5}\text{ < 2 or }\frac{x\text{ - 3}}{5}\text{ > -2} \\ We\text{ solve seperately to get two answers} \end{gathered}`
`\begin{gathered} \frac{x\text{ - 3}}{5}\text{ < 2} \\ x\text{ - 3 < 2(5)} \\ x\text{ - 3 < 10} \\ x\text{ < 10 + 3} \\ x\text{ < 13} \end{gathered}`
`\begin{gathered} \frac{x\text{ - 3}}{5}\text{ > -2 (sign changes due to the negative introduced to the right side)} \\ x\text{ - 3 > -2(5)} \\ x\text{ -3 < -10} \\ x\text{ > -10 +3} \\ x\text{ > -7} \end{gathered}`
`\begin{gathered} The\text{ solution of the inequality becomes:} \\ -7\text{ < x < 13} \\ \\ \text{In interval notation:} \\ (-7,\text{ 13)} \end{gathered}`