Question

which points are solutions to the linear inequality $y < 0.5x + 2$? select three options. $\square$ $(-3, -2)$ $\square$ $(-2, 1)$ $\square$ $(-1, -2)$ $\square$ $(-1, 2)$ $\square$ $(1, -2)$

Explanation:

Step1: Test point (-3,-2)

Substitute $x=-3, y=-2$ into $y < 0.5x + 2$:

$$\begin{align} -2 &< 0.5(-3) + 2 \\ -2 &< -1.5 + 2 \\ -2 &< 0.5 \end{align}$$

This is true.

Step2: Test point (-2,1)

Substitute $x=-2, y=1$ into $y < 0.5x + 2$:

$$\begin{align} 1 &< 0.5(-2) + 2 \\ 1 &< -1 + 2 \\ 1 &< 1 \end{align}$$

This is false.

Step3: Test point (-1,-2)

Substitute $x=-1, y=-2$ into $y < 0.5x + 2$:

$$\begin{align} -2 &< 0.5(-1) + 2 \\ -2 &< -0.5 + 2 \\ -2 &< 1.5 \end{align}$$

This is true.

Step4: Test point (-1,2)

Substitute $x=-1, y=2$ into $y < 0.5x + 2$:

$$\begin{align} 2 &< 0.5(-1) + 2 \\ 2 &< -0.5 + 2 \\ 2 &< 1.5 \end{align}$$

This is false.

Step5: Test point (1,-2)

Substitute $x=1, y=-2$ into $y < 0.5x + 2$:

$$\begin{align} -2 &< 0.5(1) + 2 \\ -2 &< 0.5 + 2 \\ -2 &< 2.5 \end{align}$$

This is true.

Answer:

(-3, -2), (-1, -2), (1, -2)