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Solve the inequality. Graph the solution. \( \begin{array}{lll}\text { 8. }-\frac{x}{3}<2 & \text { 9. } \frac{1}{3} p \geq 4 & \text { 10. }-8<\frac{2}{3} n\end{array} \)

Ask by Dunn Rowe. in the United States
Jan 22,2025

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**Solutions:** 1. **Problem 8:** \[ -\frac{x}{3} < 2 \implies x > -6 \] - **Graph:** Open circle at -6, shading to the right. 2. **Problem 9:** \[ \frac{1}{3}p \geq 4 \implies p \geq 12 \] - **Graph:** Closed circle at 12, shading to the right. 3. **Problem 10:** \[ -8 < \frac{2}{3}n \implies n > -12 \] - **Graph:** Open circle at -12, shading to the right. **Graphical Representations:** - **Problem 8:** \( x > -6 \) - **Problem 9:** \( p \geq 12 \) - **Problem 10:** \( n > -12 \) *(Each graph shows an open circle at the boundary point and shading to the right, indicating all numbers greater than the boundary.)*

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Bonus Knowledge

Let's tackle each inequality step by step. 8. To solve \(-\frac{x}{3} < 2\): First, multiply both sides by \(-3\) (remember that multiplying by a negative reverses the inequality): \[ x > -6 \] So the solution is \( x > -6 \). 9. For \(\frac{1}{3} p \geq 4\): Multiply both sides by \(3\) to eliminate the fraction: \[ p \geq 12 \] So the solution is \( p \geq 12 \). 10. Now for \(-8 < \frac{2}{3} n\): Multiply both sides by \(\frac{3}{2}\) to solve for \(n\) (again remembering that since \(\frac{3}{2}\) is positive, the inequality stays the same): \[ -12 < n \] Or, in simpler terms: \[ n > -12 \] Now, let’s create a graph for each solution. - For \(x > -6\), graph a number line with an open circle at \(-6\) and shade to the right. - For \(p \geq 12\), graph with a closed circle at \(12\) and shade to the right. - For \(n > -12\), graph with an open circle at \(-12\) and shade to the right. Feel free to visualize these on a number line for clarity!

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