Solve for x.

Question

Graph the solution.   
negative 3x less than or equals 6
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Question content area right
Part 1
The solution is x greater than or equals
  
enter your response here.

Answer 1

To solve the inequality \(-3x \leq 6\), we will isolate \(x\).

1. Start by dividing both sides of the inequality by \(-3\). Remember that when you divide or multiply both sides of an inequality by a negative number, you need to reverse the inequality sign.

   \[ x \geq \frac{6}{-3} \]

   Simplifying the right side gives:

   \[ x \geq -2 \]

So, the solution is \(x \geq -2\).

Graphing the Solution:

To graph this inequality on a number line:

1. Draw a number line.
2. Locate \(-2\) on the number line.
3. Since the inequality is "greater than or equal to," place a closed dot or circle on \(-2\) to indicate that \(-2\) is included in the solution set.
4. Shade the portion of the number line to the right of \(-2\) to indicate that all numbers greater than \(-2\) are included in the solution.

Thus, the complete statement for the answer is:

The solution is \(x \geq -2\) (with the graph shading right from -2, including a closed dot at -2).