Question

move each inequality next to the number line it represents.
number line
inequality
$x < -2$
$x > -2$
$x \leq -2$
$x \geq -2$

Explanation:

Step1: Analyze \( x < -2 \)

• Key: Open circle (not equal), left arrow (less than).
• Match: First number line (open at \(-2\), left arrow).

Step2: Analyze \( x > -2 \)

• Key: Open circle, right arrow (greater than).
• Match: Fourth number line (open at \(-2\), right arrow).

Step3: Analyze \( x \leq -2 \)

• Key: Closed circle (equal), left arrow (less than or equal).
• Match: Third number line (closed at \(-2\), left arrow).

Step4: Analyze \( x \geq -2 \)

• Key: Closed circle, right arrow (greater than or equal).
• Match: Second number line (closed at \(-2\), right arrow).

Answer:

To solve this, we analyze each number line and inequality:

For \( x < -2 \):

• The number line should have an open circle at \(-2\) (since \( x \) is not equal to \(-2\)) and the arrow pointing to the left (for values less than \(-2\)). Looking at the number lines, the first number line (from the left) has an open circle at \(-2\) and the arrow pointing left. So \( x < -2 \) matches the first number line.

For \( x > -2 \):

• The number line should have an open circle at \(-2\) and the arrow pointing to the right (for values greater than \(-2\)). The fourth number line (from the left) has an open circle at \(-2\) and the arrow pointing right. So \( x > -2 \) matches the fourth number line.

For \( x \leq -2 \):

• The number line should have a closed circle at \(-2\) (since \( x \) can be equal to \(-2\)) and the arrow pointing to the left (for values less than or equal to \(-2\)). The third number line (from the left) has a closed circle at \(-2\) and the arrow pointing left. So \( x \leq -2 \) matches the third number line.

For \( x \geq -2 \):

• The number line should have a closed circle at \(-2\) and the arrow pointing to the right (for values greater than or equal to \(-2\)). The second number line (from the left) has a closed circle at \(-2\) and the arrow pointing right. So \( x \geq -2 \) matches the second number line.