Question

Can you please explain how I can solve the following questions?

Answer 1

To graph lineal inequalities:

1. Solve in the inequality the variable y:

`3x+3y>12`

- Substract 3x in both sides of the inequation:

`\begin{gathered} 3x-3x+3y>-3x+12 \\ 3x>-3x+12 \end{gathered}`

- Divide both sides of the inequation into 3:

`\begin{gathered} (3)/(3)x>((-3x+12))/(3) \\ \\ x>-(3)/(3)x+(12)/(3) \\ \\ x>-x+4 \end{gathered}`

2. Find two points in the line that limits the inequality

The line is y=-x+4

Find y when x=0

`\begin{gathered} y=-0+4 \\ y=4 \end{gathered}`

Find x when y=0:

`\begin{gathered} 0=-x+4 \\ 0+x=-x+x+4 \\ x=4 \end{gathered}`

You have the next two points in the line: (0,4) and (4,0)

3. Put the points in the plane and draw the line that passes trought those points:

When the inequality is < or > you draw a dotted line (the line is not part of the solution)

When the inequality is ≥ or ≤ you draw a line (it is part of the solution)

4. Shadow the area that correspond to the inequality:

When the inequality is < or ≤ you shadow the area under the line

When the inequality is > or ≥ you shadow the area over the line.

In this case as the inequality symbol is > you draw a dotted line and shadow the area over the line. You get the next graph: