Question

which worked - out problem correctly shows how to use the test point (-1, 2) in the inequality y < -x - 0.6?
-1 < -(2) - 0.6
-1 < -2 - 0.6
-1 < -2.6
false; the region containing (-1, 2) is not the solution set
2 < -(-1) - 0.6
2 < 1 - 0.6
2 < 0.4
false; the region containing (-1, 2) is not the solution set
2 < -1 - 0.6
2 < -1 + -0.6
2 < -1.6
true; the region containing (-1, 2) is the solution set
-1 < (-2) - 0.6
-1 < -2 - 0.6
-1 < -2.6
true; the region containing (-1, 2) is the solution set

Explanation:

Step1: Identify test point values

The test point is $(-1, 2)$, so $x=-1$, $y=2$.

Step2: Substitute into inequality

Substitute $x=-1$, $y=2$ into $y < -x - 0.6$:
$2 < -(-1) - 0.6$

Step3: Simplify right-hand side

Calculate $-(-1) = 1$, so:
$2 < 1 - 0.6$
$2 < 0.4$

Step4: Evaluate the inequality

$2 < 0.4$ is false, so the region containing $(-1, 2)$ is not the solution set.

Answer:

$2 < -(-1) - 0.6$
$2 < 1 - 0.6$
$2 < 0.4$
False; the region containing $(-1, 2)$ is not the solution set