# SOLUTION: <pre>Solve the inequality and graph the solution on a real number line 1/x <u>></u> 1/(x+3)</pre>

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 Algebra: Inequalities, trichotomy Solvers Lessons Answers archive Quiz In Depth

 Question 44639This question is from textbook College Algebra : ```Solve the inequality and graph the solution on a real number line 1/x > 1/(x+3)```This question is from textbook College Algebra Answer by AnlytcPhil(1277)   (Show Source): You can put this solution on YOUR website!```Solve the inequality and graph the solution on a real number line 1/x > 1/(x+3) 1/x - 1/(x+3) > 0 (x+3) - x --------- > 0 x(x+3) 3 -------- > 0 x(x+3) The critical values are x=0 and x=-3 Mark those on a number line: <----------o--------o-----------> -3 0 Choose a value left of (less than) -3, say -4 and substitute it into 3 -------- x(x+3) 3 3 ---------- = ---- which is positive -4(-4+3) 4 so our number line becomes ++++++++++ <----------o--------o-----------> -3 0 Choose a value between -3 and 0, say -1 and substitute it in 3 -------- x(x+3) 3 3 ---------- = ---- which is negative -1(-1+3) -2 so our number line becomes ++++++++++ -------- <----------o--------o-----------> -3 0 Choose a value right of 0, that is , greater than 0, say 1, and substitute it into 3 -------- x(x+3) 3 3 ---------- = ---- which is positive 1(1+3) 4 so our number line becomes ++++++++++ -------- +++++++++++ <----------o--------o-----------> -3 0 The expression 3 -------- x(x+3) is not defined at the endpoints 0 or -3, so the solution, since 3 -------- > 0 x(x+3) requires the left side to be non-negative, the solution set in interval notation is (-oo, -3) U (0, oo) Edwin AnlytcPhil@aol.com```