Answer:
-4 5/6 < x < 4 1/6
Step-by-step explanation:
This inequality can be solved by dividing by 2, then subtracing 1/3 (after unfolding).
... 2|x + 1/3| < 9 . . . . . . given
... |x + 1/3| < 4 1/2 . . . . divide by 2
... -4 1/2 < x + 1/3 < 4 1/2 . . . . . "unfold" the inequality, recognizing the meaning of the absolute value
... -4 5/6 < x < 4 1/6 . . . . . . . . subtract 1/3.
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The first graph is of the solution. The second graph is of the function on the left, which is what you get when you subtract 9 from the inequality. Many graphing calculators make x-intercepts easy to find, so it is convenient to put the expression in a form that makes the x-intercepts be the answers of interest. Here, the curve is below the x-axis (< 0) between the intercepts, hence that is the solution space for x.
... 2|x +1/3| -9 < 0
