Question

Graph the solution set of the following linear inequality:2y < 2x + 4AnswerKeypadKeyboard ShortcutsThe line will be drawn once all required data is provided and will update whenever a value is updated. Theregions will be added once the line is drawn.101Choose the type of boundary line:Dashed -O Solid (-) O--)5Enter two points on the boundary line:10--5310Select the region you wish to be shaded:5ОАOB19

Answer 1

Explanation

$2y<2x+4$

To graph an inequality, treat the <, ≤, >, or ≥ sign as an = sign, and graph the equation. If the inequality is < or >, graph the equation as a dotted line. If the inequality is ≤ or ≥, graph the equation as a solid line.

Step 1

a)isolate y in the inequality

$\begin{gathered} 2y<2x+4 \\ \text{divide both sides by 2} \\ \frac{2y}{2}<\frac{2x+4}{2} \\ y=\frac{2x+4}{2}=\frac{2x}{2}+\frac{4}{2} \\ y=x+2\Rightarrow\text{ Line} \end{gathered}$

Step 2

draw the line:to do that we need 2 points from the line

a) for x=0

$\begin{gathered} y=x+2 \\ \text{replace} \\ y=0+2=2 \\ \text{hence} \\ \text{Point 1(0,2)} \end{gathered}$

b)for x= 3

$\begin{gathered} y=x+2 \\ \text{replace} \\ y=3+2=5 \\ \text{hence} \\ \text{Point 1(3,5)} \end{gathered}$

c) draw a dotted line that passes trought point 1( 0,2) and point 2 (3,5)

d) as we are searching for the y values smaler thatn the function

[tex]ywe need to take the area under the line

therefore, the answer is