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The solution is -7
Ask by Ward Tucker. in South Africa
Mar 08,2025

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Answer

The solution in interval notation is \((-7, -2)\).

Solution

To solve the inequality \(-7 < w < -2\), we can break it down into two parts: 1. **Understanding the inequality**: The expression \(-7 < w < -2\) means that \(w\) is greater than \(-7\) and less than \(-2\). 2. **Interval notation**: In interval notation, we represent the solution as an interval that includes all numbers between \(-7\) and \(-2\), but does not include the endpoints themselves since the inequalities are strict (i.e., they do not include equal to). Thus, the interval notation for the solution is: \[ (-7, -2) \] This indicates that \(w\) can take any value greater than \(-7\) and less than \(-2\).

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Bonus Knowledge

To solve the compound inequality \(-7 < w < -2\), you can break it down into two parts. Start by isolating \(w\) between the two values. The left part, \(-7 < w\), tells us that \(w\) must be greater than -7. The right part, \(w < -2\), indicates that \(w\) must also be less than -2. In interval notation, this solution is expressed as \((-7, -2)\), which means that \(w\) includes all numbers greater than -7 and less than -2 but does not include the endpoints themselves. Want to converse about similar inequalities? You got it! Pellet those inequalities, and you'll unlock the secrets to solving more complex ranges. Keep practicing, and soon, interval notation will be your new language!

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