Here are the steps in graphing the linear inequality.
1. Convert the linear inequality into a slope-intercept form or by converting the equation into y = or y > or y <.
a. Isolate the variable "y" on the left side of the inequality by subtracting 5x on both sides of the inequality.
[tex]5x-5x+2y<10-5x[/tex][tex]2y<10-5x[/tex]
b. Divide both sides of the inequality by 2.
[tex]\frac{2y}{2}<\frac{10}{2}-\frac{5x}{2}[/tex][tex]y<5-\frac{5}{2}x[/tex]
c. Rearrange the terms on the right side.
[tex]y<-\frac{5}{2}x+5[/tex]
2. From the converted inequality, we can see that the slope is -5/2 while the y-intercept is 5.
Let's plot the y-intercept at (0, 5) first.
Then, using the slope -5/2, let's find another point that is 5 units downward and 2 units to the right of the y-intercept.
3. Connect the dots using a dotted line since the inequality symbol is <. Then, shade the part below the line since the inequality symbol is "less than".
The final graph of the given linear inequality is shown below:
