Questions: The graph of 5x-2y<24 has a boundary line.

The graph of 5x-2y<24 has a boundary line.
Transcript text: The graph of $5 x-2 y<24$ has a $\square$ boundary line.
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Solution

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Solution Steps

To determine the type of boundary line for the inequality \(5x - 2y < 24\), we need to consider the nature of the inequality. If the inequality is strict (i.e., uses "<" or ">"), the boundary line is dashed. If the inequality is non-strict (i.e., uses "≤" or "≥"), the boundary line is solid.

Solution Approach
  • Identify the type of inequality.
  • Determine the corresponding boundary line type based on the inequality.
Step 1: Identify the Inequality

The given inequality is \(5x - 2y < 24\). This is a linear inequality in two variables.

Step 2: Determine the Type of Boundary Line

Since the inequality is strict (using "<"), the boundary line will not include the points on the line itself. Therefore, the boundary line is dashed.

Final Answer

The graph of \(5x - 2y < 24\) has a dashed boundary line. Thus, the answer is \(\boxed{\text{dashed}}\).

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