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Question 421215: Hi! I would really appreciate some help solving these problems. "Graph the solution set of the following linear inequality 2(y+3)< -x? There is also this one I am stumped on as well, -7y-8x(is greater than or equal to)-7y+56? I know what type of line they are asking for, Dotted or solid, but when it comes to answering what points they want me to plot I am lost.
Thank you in advance for taking the time to answer =)
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! in order to graph the solution, you have to solve for y.
for example:
your first equation is 2 * (y+3) < -x
divide both sides of the equation by 2 to get:
y + 3 < -x/2
subtract 3 from both sides of the equation to get:
y < -x/2 - 3
now you can graph the equation.
to graph it, set the equation to an equality rather than an inequality.
you will graph y = -x/2 - 3
graph of that equation is shown below:
since your inequality states that y < -x/2 - 3, than any value of y that is in the area underneath the line y = -x/2 - 3 will satisfy the equation.
for example:
when x = 2, y = -2/2 - 3 = -1 - 3 = -4
when x = 2, any value of y < -4 will satisfy the equation of y < -x/2 - 3.
by shading the area underneath the line of the equation, you indicate the possible values that y can take that satisfy the equation y < -x/2 - 3.
not that y < -4 will satisfy the equation when x = 2, but will not satisfy the equation when x = 4.
when x = 4, the line of the equation is equal to -4/2 - 3 = -2 - 3 = -5.
when x = 4, y needs to be less than -5 to satisfy the equation.
i redrew the equation of the line y = -x/2 - 3 and added lines at y = -4 and y = -5 so you can see that more clearly.
bottom line:
you solve for y so you can graph the inequality.
you graph the equality.
you shade the area that supports the inequality.
in this case, the shaded area would be underneath the line because the inequality indicates less than.
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