Questions: Linear Equations and Inequalities Set-builder and interval notation Graph the set x x>3 on the number line. Then, write the set using interval notation. x x>3=

Linear Equations and Inequalities Set-builder and interval notation Graph the set x x>3 on the number line. Then, write the set using interval notation. x x>3=
Transcript text: Linear Equations and Inequalities Set-builder and interval notation Graph the set $\{x \mid x>3\}$ on the number line. Then, write the set using interval notation. \[ \{x \mid x>3\}= \] $\square$
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Solution

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Solution Steps

Step 1: Understand the Inequality

The given inequality is \( x > 3 \). This means we are looking for all values of \( x \) that are greater than 3.

Step 2: Graph the Inequality on the Number Line

To graph \( x > 3 \) on the number line:

  • Draw an open circle at 3 to indicate that 3 is not included in the set.
  • Shade the number line to the right of 3 to show all numbers greater than 3.
Step 3: Write the Set Using Interval Notation

In interval notation, \( x > 3 \) is represented as \( (3, \infty) \). This notation indicates that the interval starts just after 3 and extends to positive infinity, not including 3 itself.

Final Answer

  • Graph: Open circle at 3, shading to the right.
  • Interval Notation: \( (3, \infty) \)
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