You can put this solution on YOUR website! Given:
.
.
Graph this expression.
.
Begin by assuming this is an equation and let's get it into the slope intercept form.
By assuming it's an equation we can operate on it in the normal way of applying mathematical
operations. The only thing we have to be careful of is if we multiply or divide both sides
of our "equation" by a negative number we have to reverse the direction of the inequality
sign.
.
The next thing we can do is subtract 3x from both sides to eliminate the 3x on the left side.
The result of this is that the "equation" becomes:
.
.
You may now recognize that this is in slope-intercept form. The graph intercepts the
y-axis at +5 and the slope is down and to the right (because the slope is negative)
at a rate of -3 ... meaning that for every one unit the graph goes to the right, it goes down
3 units in the vertical direction.
.
Graph this line. When you do it should look like:
.
.
Next what you want to do is to shade in the area below the graphed line, and shade it
so it includes the graphed line but nothing above it. Now you can claim that any value
of y that satisfies the original equality is in that shaded area (including on the graphed line)
because that shaded area identifies where any point in that area has a y value that is less than
or equal to as represented by the graphed line.
.
Hope that this process gives you some insight into how inequalities can be graphed.
(