Solve the inequality. Write the solution set in interval notation.

Question

Solve the inequality. Write the solution set in interval notation. $$ 11 \leq 6(n+4)-4 n $$

UpStudy AI · Accepted Answer

To solve the inequality $$ 11 \leq 6(n+4) - 4n $$:

1. **Expand and simplify the right-hand side:**
   $$
   6(n + 4) - 4n = 6n + 24 - 4n = 2n + 24
   $$
   
2. **Rewrite the inequality:**
   $$
   11 \leq 2n + 24
   $$
   
3. **Isolate $$ n $$:**
   $$
   11 - 24 \leq 2n \quad \Rightarrow \quad -13 \leq 2n
   $$
   
4. **Divide both sides by 2:**
   $$
   -\frac{13}{2} \leq n
   $$
   
5. **Express the solution in interval notation:**
   $$
   \left[ -\frac{13}{2}, \infty \right)
   $$

**Final Answer:**

$$\left[ -\dfrac{13}{2},\ \infty\, \right)$$
The solution is $$ n \geq -\frac{13}{2} $$, which in interval notation is $$\left[ -\frac{13}{2}, \infty \right)$$.

Solve the inequality. Write the solution set in interval notation.

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