Question

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

Explanation:

Step1: Substitute (-3,-2) into inequality

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

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

This is true, so (-3,-2) is a solution.

Step2: Substitute (-2,1) into inequality

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

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

This is false, so (-2,1) is not a solution.

Step3: Substitute (-1,-2) into inequality

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

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

This is true, so (-1,-2) is a solution.

Step4: Substitute (-1,2) into inequality

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

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

This is false, so (-1,2) is not a solution.

Step5: Substitute (1,-2) into inequality

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

$$\begin{align} -2 &< 0.5\times1+2 \\ -2 &< 0.5+2 \\ -2 &< 2.5 \end{align}$$

This is true, so (1,-2) is a solution.

Answer:

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