Solve each inequality in Exercises 86–91 using a graphing utility...

Question

Solve each inequality in Exercises 86–91 using a graphing utility.

1/(x + 1) ≤ 2/(x + 4)

Accepted Answer

Hey everyone here we are asked to use a graphing utility to solve the inequality of one divided by the quantity of X plus four is less than or equal to two divided by the quantity of X plus eight. Now to graph this inequality you just want to graph each expression individually and compare. So I'm going to let my first expression be green and B Y is equal to one divided by the quantity of X plus four. And then my red will be the second expression and be graphed as Y is equal to two divided by the quantity of X plus eight. And after graphing we are able to assess and solve the given problem. So we can see here that this green which is the expression that should be less than or equal to is less than or below the red graph from negative eight to negative four. So one of our solutions will be negative eight to negative four. But we're not done yet. We have to notice that these graphs do intersect at X equals zero. And then we can see if you look closely that green is less than the red or below the red up until infinity. So it goes from zero which is included within a bracket to positive infinity. And again, zero is with a bracket because it is included within the solution and therefore our answer here is choice C with an answer of negative eight to negative four and zero included to positive infinity. Thanks for watching. I hope you found this video helpful and I'll see you again next time

Solve each inequality in Exercises 86–91 using a graphing utility. 1/(x + 1) ≤ 2/(x + 4)

Key Concepts

Inequalities

Rational Functions

Graphing Utilities

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