Question
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Graph the inequality. \( x<-9 \)

Ask by Donnelly Lowe. in the United States
Jan 25,2025

Real Tutor Solution

Tutor-Verified Answer

Answer

To graph \( x < -9 \), draw a dashed vertical line at \( x = -9 \) and shade the area to the left of this line.

Solution

To graph the inequality \( x < -9 \), follow these steps: 1. **Identify the boundary line**: The boundary for the inequality is the vertical line \( x = -9 \). This line will be dashed because the inequality is strict (it does not include the value -9). 2. **Determine the solution region**: Since the inequality is \( x < -9 \), we are interested in the region to the left of the line \( x = -9 \). 3. **Graphing**: - Draw a dashed vertical line at \( x = -9 \). - Shade the area to the left of this line to indicate all the values of \( x \) that satisfy the inequality. This graph visually represents all the values of \( x \) that are less than -9.

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Beyond the Answer

Imagine a number line stretching out before you! To graph the inequality \( x < -9 \), you'll first find the point -9 on that line. The next step is to draw an open circle around -9, indicating that this point itself is not included in the solution. Then, shade everything to the left of -9 to show all the numbers less than -9. Voilà! You've graphically represented this inequality, illustrating that x can be any value smaller than -9. In real life, think of an exclusive club! The entry requirement is being less than a certain age: let's say 9. Anyone below that age is welcome, but those who are 9 or older cannot enter. Just as in the graph where -9 is not included, the club has a strict policy against allowing those at that age! This makes it clear that the values you’re interested in are only those that satisfy the inequality.

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