SOLUTION: solve and graph the inequality. Can someone help me answer this? x+3/x less than or equal to -2

Question 23383: solve and graph the inequality. Can someone help me answer this?
x+3/x less than or equal to -2

Answer by rapaljer(4671) (Show Source): You can put this solution on YOUR website!
This one would be

The first step is probably to set this inequality to zero by adding +2 to each side. WARNING: DO NOT MULTIPLY BOTH SIDES OF THE INEQUALITY BY A VARIABLE x!!

As I said, do NOT multiply both sides of the inequality by x, but you CAN find a common denominator of x, and express the left side as a single fraction! That is allowed, and it will help solve the problem.

Now draw the graph. The numerator does not factor, and probably does NOT have any real roots. The denominator will equal zero at x=0, so this is an ASYMPTOTE. With this done, now draw the graph, either with a graphing calculator or with the calculator in algebra.com. For this, you can use the original form of the inequality after you set it equal to zero, :

In this problem since it is a LESS THAN OR EQUAL TO problem, you will be looking for all values ON OR BELOW the x-axis. This will be the values of x to the left of the y-axis. Because the problem says "less than or EQUAL to", you would normally be INCLUDING THE ENDPOINTS. However, you NEVER include DENOMINATOR endpoints, since division by zero is NEVER allowed. So the final answer is x<0. Interval notation is (-inf, 0).

R^2 at SCC

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