Questions: Express the graph shown in color using interval notation. Also express the graph as an inequality involving x.

Express the graph shown in color using interval notation. Also express the graph as an inequality involving x.
Transcript text: Express the graph shown in color using interval notation. Also express the graph as an inequality involving $x$.
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Solution

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Solution Steps

Step 1: Identify the Interval

The graph shows a number line with a shaded region starting from 5 and extending to the right indefinitely. This indicates that the interval starts at 5 and goes to positive infinity.

Step 2: Determine the Type of Interval

Since the shaded region starts at 5 and includes 5 (indicated by the solid dot), the interval is closed at 5. The interval extends to positive infinity, which is always open.

Step 3: Write the Interval in Interval Notation

The interval notation for a closed interval starting at 5 and extending to positive infinity is \([5, \infty)\).

Step 4: Express the Inequality

The inequality that represents this interval is \(x \geq 5\).

Final Answer

  • Interval Notation: \([5, \infty)\)
  • Inequality: \(x \geq 5\)
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