Question

match each expression with a number line graph.
$xleq - 2$
$x < 1$
$x > - 2$
$xgeq - 2$
$xleq 1$
$x > 1$

Explanation:

Step1: Analyze $x\leq - 2$

This includes -2 and all numbers to the left of -2 on the number - line. The graph has a closed - circle at -2 and a line extending to the left.

Step2: Analyze $x < 1$

This includes all numbers less than 1. The graph has an open - circle at 1 and a line extending to the left.

Step3: Analyze $x>-2$

This includes all numbers greater than -2. The graph has an open - circle at -2 and a line extending to the right.

Step4: Analyze $x\geq - 2$

This includes -2 and all numbers to the right of -2 on the number - line. The graph has a closed - circle at -2 and a line extending to the right.

Step5: Analyze $x\leq 1$

This includes 1 and all numbers to the left of 1 on the number - line. The graph has a closed - circle at 1 and a line extending to the left.

Step6: Analyze $x > 1$

This includes all numbers greater than 1. The graph has an open - circle at 1 and a line extending to the right.

Answer:

$x\leq - 2$ matches the graph with a closed - circle at -2 and a line extending to the left.
$x < 1$ matches the graph with an open - circle at 1 and a line extending to the left.
$x>-2$ matches the graph with an open - circle at -2 and a line extending to the right.
$x\geq - 2$ matches the graph with a closed - circle at -2 and a line extending to the right.
$x\leq 1$ matches the graph with a closed - circle at 1 and a line extending to the left.
$x > 1$ matches the graph with an open - circle at 1 and a line extending to the right.