Identify the boundaries of the solution of this inequality
[3x]

Question

Identify the boundaries of the solution of this inequality
[3x]<9
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whpalmer4 · Answer

Turn the inequality into an equality by changing to an equals sign.  Solve.  Now you've got your boundary point(s).

anonymous · Answer

how do you do that?

whpalmer4 · Answer

Your inequality is $$|3x| < 9$$right?

anonymous · Answer

yea

whpalmer4 · Answer

Change it to be $$|3x|=9$$Divide both sides by 3
$$|x| = 3$$$$x = \pm 3$$So the boundaries are at x = 3 and x = -3.  Now, to find the actual included area(s), we test some points and see if they satisfy the original inequality.  I like to use 0 as a test point, because the arithmetic is usually easy.  

$$|3*0| < 9$$Well, yeah, 0 is less than 9, so 0 is in the part that satisfies the inequality.  Because 0 is between x = 3 and x = -3, that means the part of the number line that satisfies the inequality is the area between x = 3 and x = -3, not including the boundary points.  If we had instead $|3x| \le 9$ we would include the boundary points (which are included if the inequality includes the equals sign).  We signify that the point is not included by marking it with a circle instead of a filled-in dot.