Question

In the following exercises, determine whether each ordered pair is a solution to the given inequality.

Determine whether each ordered pair is a solution to the inequality :

$y<3x+2$

ⓐ (0, 3) ⓑ (−3, −2) ⓒ (−2, 0) ⓓ (0, 0) ⓔ (−1, 4)

Short answer

(a)$(0,3)$is not a solution

(b)$(-3,-2)$is not a solution

(c)$(-2,0)$is not a solution

(d)$(0,0)$is a solution

(e)$(-1,4)$is not a solution

Step-by-step solution

Part (a) Step 1: Given information

$y<3x+2$

To check whether$(0,3)$is a solution to the equation

Part (a) Step 2: Calculation

Replace the value of x and y in $y<3x+2$

Here $x=0,y=3$

$$\begin{gathered} 3<3\times 0+2 \\ 3<0+2 \\ 3\nless 2 \end{gathered}$$

The point$(0,3)$is not a solution to$y<3x+2$

Part (b) Step 1: Given information

$y<3x+2$

To check whether $(-3,-2)$is a solution to the equation

Part (b) Step 2: Calculation

Replace the values of x and y in $y<3x+2$

Here $x=-3,y=-2$

role="math" localid="1645952636841" $$\begin{gathered} -2<3\times (-3)+2 \\ -2<-9+2 \\ -2\nless -7 \end{gathered}$$

The point$(-3,-2)$is not a solution to$y<3x+2$

Part (c) Step 1: Given information

$y<3x+2$

To check whether $(-2,0)$is a solution to the equation

Part (c) Step 2: Calculation

Replace the value of x and y in $y<3x+2$

Here $x=-2,y=0$

$$\begin{gathered} 0<3\times (-2)+2 \\ 0<-6+2 \\ 0\nless -4 \end{gathered}$$

The point $(-2,0)$is not a solution to$y<3x+2$

Part (d) Step 1: given information

$y<3x+2$

To check whether$(0,0)$is a solution to the equation

Part (d) Step 2: Calculation

Replace the values of x and y in $y<3x+2$

Here $x=0,y=0$

$$\begin{gathered} 0<3\times 0+2 \\ 0<0+2 \\ 0<2 \end{gathered}$$

The point$(0,0)$is a solution to$y<3x+2$

Part (e) Step 1: Given information

$y<3x+2$

To check whether$(-1,4)$is a solution to the equation

Part (e) Step 2: Calculation

Replace the values of x and y in $y<3x+2$

Here $x=-1,y=4$

$$\begin{gathered} 4<3\times (-1)+2 \\ 4<-3+2 \\ 3\nless -1 \end{gathered}$$

The point $(-1,4)$is a not solution to $y<3x+2$