Question

graph the compound inequality on the number line.
( x geq 7 ) or ( x < 5 )

Explanation:

Step1: Analyze \( x < 5 \)

For \( x < 5 \), we use an open circle at \( 5 \) (since \( x \) is not equal to \( 5 \)) and draw an arrow to the left (towards negative infinity) to represent all numbers less than \( 5 \).

Step2: Analyze \( x \geq 7 \)

For \( x \geq 7 \), we use a closed circle at \( 7 \) (since \( x \) is equal to \( 7 \)) and draw an arrow to the right (towards positive infinity) to represent all numbers greater than or equal to \( 7 \).

Step3: Combine the two graphs

Since the compound inequality is "or", we combine the two graphs. So we have an open circle at \( 5 \) with a left - pointing arrow and a closed circle at \( 7 \) with a right - pointing arrow on the number line.

Graph Description (for the number line):

• For \( x < 5 \): Place an open circle (the empty circle icon) at \( 5 \) on the number line and draw an arrow starting from this open circle going to the left (towards \( - 10,-9,\cdots\)).
• For \( x\geq7 \): Place a closed circle (the filled - in circle icon) at \( 7 \) on the number line and draw an arrow starting from this closed circle going to the right (towards \( 8,9,10,\cdots\)).

(Note: Since the question asks to graph, and we can't directly draw here, but we can describe the steps to graph. If we were to represent the final graph in terms of the given tools, we would use the open circle at \( 5 \), the closed circle at \( 7 \), and the arrow tools to draw the respective arrows.)

Answer:

Step1: Analyze \( x < 5 \)

For \( x < 5 \), we use an open circle at \( 5 \) (since \( x \) is not equal to \( 5 \)) and draw an arrow to the left (towards negative infinity) to represent all numbers less than \( 5 \).

Step2: Analyze \( x \geq 7 \)

For \( x \geq 7 \), we use a closed circle at \( 7 \) (since \( x \) is equal to \( 7 \)) and draw an arrow to the right (towards positive infinity) to represent all numbers greater than or equal to \( 7 \).

Step3: Combine the two graphs

Since the compound inequality is "or", we combine the two graphs. So we have an open circle at \( 5 \) with a left - pointing arrow and a closed circle at \( 7 \) with a right - pointing arrow on the number line.

Graph Description (for the number line):

• For \( x < 5 \): Place an open circle (the empty circle icon) at \( 5 \) on the number line and draw an arrow starting from this open circle going to the left (towards \( - 10,-9,\cdots\)).
• For \( x\geq7 \): Place a closed circle (the filled - in circle icon) at \( 7 \) on the number line and draw an arrow starting from this closed circle going to the right (towards \( 8,9,10,\cdots\)).

(Note: Since the question asks to graph, and we can't directly draw here, but we can describe the steps to graph. If we were to represent the final graph in terms of the given tools, we would use the open circle at \( 5 \), the closed circle at \( 7 \), and the arrow tools to draw the respective arrows.)