Explain what type (solid or dashed) and shading (above or below) for each in equality symbol:

Question

yoooweslime · Answer

there is no picture

Extrinix · Answer

Then provide the symbols please.

darkknight · Answer

extrinix, you have to help them explain the solid/dash and shading for each symbol. Will leave to you

darkknight · Answer

For example $$>,\le,\ge,<,$$

Extrinix · Answer

Oh, I missed the "inequality" part, oops.

darkknight · Answer

You're good, they did a typo, continue

Extrinix · Answer

So, let's begin by identifying whether each symbol does,

$\le$ - Less Than or Equal to:
So, this means any number less than or equal to a number (ex. -1 $\le$ 0),

$\ge$ - Greater Than or Equal to:
This means any number greater than or equal to a number (ex. 1 $\ge$ 0),

$\lt$ - Less Than:
This means any number less than a number, but not equal to it 
(ex. -1 $\lt$ 0, but not 0 $\lt$ 0)

$\gt$ - Greater Than:
This means any number greater than a number, but not equal to it
(ex. 1 $\gt$ 0, but not 0 $\gt$ 0)

Now, to figure out whether the line is solid or dashed and shaded or not,
Solid Circle ($\bullet$) - Contains the origin number
Empty Circle ($\circ$) - Does NOT contain the origin number
Solid Line (---) - Includes origin number
Dashed Line (- - -) - Does NOT contain the origin number

So, from that you should be able to identify each symbol whether they are,
Solid Circle / Solid Line
Solid Circle / Dashed Line
Empty Circle / Solid Line
Empty Circle / Dashed Line

darkknight · Answer

While that does outline the basis it doesn't necessarily give enough of a clue about the shading part, most likely the user knows what less than and greater than means but they need a graphical example. Since Extrinix has already provided that, no need to repeat it, but lets look at 1 example to give you an idea. Say our equation is $$y \le-3x$$ we graph the line y = 3x and since our inequality is greater than OR equal to we have a solid line because we are also including that equal to part. Now this is how y = -3x looks like |dw:1621961278189:dw|
Think about it this way, what region should be shaded? $$y \le-3x$$ in the sense of words means that the y-value will be less than or equal to the line resulted by -3x

darkknight · Answer

We have a solid line which denotes the "or equal to" part and to represent that y is less than we shade UNDER the line, or like |dw:1621961431434:dw|10/10 shading (:

darkknight · Answer

Do note that was a less than and equal to, so we used a solid line and shaded under, think of examples such as $$y>x, y \ge x, y <x$$ to determine which region is shaded and whether the line is solid or dashed

darkknight · Answer

If an inequality is also including the number use a solid line, if not then a dashed line

Extrinix · Answer

Thank you @darkknight , forgot to add the shading part.