Solve and graph the solution to the inequality −6n+3≥21

Question

−
6
𝑛
+
3
≥
21
on your own paper or device. In the box below, give the solution to the inequality and describe how/.

Answer 1

To solve the inequality \(-6n + 3 \geq 21\), let's follow these steps:

1. Isolate the Variable: We want to isolate \(n\). Start by subtracting 3 from both sides of the inequality. \[ -6n + 3 - 3 \geq 21 - 3 \] This simplifies to: \[ -6n \geq 18 \]

2. Divide by \(-6\): Next, we divide both sides of the inequality by \(-6\). Remember that when you divide or multiply both sides of an inequality by a negative number, you must reverse the inequality symbol. \[ n \leq \frac{18}{-6} \] Simplifying this gives: \[ n \leq -3 \]

3. Solution: The solution to the inequality is: \[ n \leq -3 \]

4. Graphing the Solution: To graph the solution on a number line:

   • Draw a number line with enough space to include \(-3\).
   • Place a solid dot on \(-3\) to indicate that \(-3\) is included in the solution.
   • Shade the line to the left of \(-3\) to show that all numbers less than or equal to \(-3\) are part of the solution.

Summary:

The solution to the inequality is \(n \leq -3\), and on the graph, you will have a solid dot at \(-3\) and shading to the left, indicating that all values lesser than or equal to \(-3\) satisfy the inequality.