Is 5 a solution to $$ -3 x+2 \leq 11 $$ ? Use a number line to prove your answer.

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1. **Substitute $$ x=5 $$ into the inequality**  
   The inequality is  
   $$
   -3x + 2 \leq 11
   $$  
   Substitute $$ x = 5 $$:  
   $$
   -3(5) + 2 = -15 + 2 = -13
   $$  
   Since  
   $$
   -13 \leq 11,
   $$  
   $$ x = 5 $$ satisfies the inequality.

2. **Solve the inequality to find the solution set**  
   Start with:  
   $$
   -3x + 2 \leq 11
   $$  
   Subtract 2 from both sides:  
   $$
   -3x \leq 9
   $$  
   Divide both sides by $$-3$$ (remember to reverse the inequality sign when dividing by a negative number):  
   $$
   x \geq -3
   $$  
   Thus, the solution set is all $$ x $$ such that  
   $$
   x \geq -3.
   $$

3. **Number line proof**  
   The solution $$ x \geq -3 $$ is represented on a number line as follows:

$$
   \text{Number Line:} \quad \ldots \,\, \color{blue}{\bullet} \,\, \longrightarrow \,\, 
   $$
   
   $$
   \begin{array}{ccccccccccc}
   \ldots & -5 & -4 & \boxed{-3} & -2 & -1 & 0 & 1 & 2 & \ldots
   \end{array}
   $$

- The boxed point at $$-3$$ (or a closed dot) represents that $$-3$$ is included.
   - The arrow to the right indicates that all numbers greater than $$-3$$ are in the solution set.

Since $$ 5 $$ is to the right of $$-3$$, it belongs to the solution set.

4. **Conclusion**  
   Yes, $$ 5 $$ is a solution to $$ -3x + 2 \leq 11 $$.
$$ 5 $$ is a solution to the inequality $$ -3x + 2 \leq 11 $$.

Is 5 a solution to ? Use a number line to prove your answer.

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