SOLUTION: slove inequality. State the solution set in interval notation and sketch its graph. -3/8 >or= -1/4x + 1/8 < 5/8

Algebra ->  Inequalities -> SOLUTION: slove inequality. State the solution set in interval notation and sketch its graph. -3/8 >or= -1/4x + 1/8 < 5/8      Log On


   

Question 83411: slove inequality. State the solution set in interval notation and sketch its graph.
-3/8 >or= -1/4x + 1/8 < 5/8
Answer by rapaljer(4671) About Me  (Show Source):
You can put this solution on YOUR website!
The tradition in math is that for double inequalities such as this to be meaningful, the inequality signs must go in the same direction. Is it possible that you miscopied this one? I'm thinking that it should be written this way:
+-3%2F8+%3C=+%28-1%2F4%29x+%2B+1%2F8+%3C+5%2F8+

If so, then begin by multiplying each part of the inequality by the LCD which is 8.
+-3%2F8+%3C=+%28-1%2F4%29x+%2B+1%2F8+%3C+5%2F8+
+8%2A%28-3%2F8%29+%3C=+8%2A%28%28-1%2F4%29x+%2B+1%2F8+%29%3C8%2A%28+5%2F8+%29
-3+%3C=-2x+%2B1+%3C5+

Next, subtract 1 from each part:
-3-1+%3C=-2x+%2B1-1+%3C5-1+
-4+%3C=-2x+%3C4+

This is the important step! Divide each part by -2. Since you are dividing by a negative number, you must REVERSE the INEQUALITY SIGNS!!
%28-4%29%2F-2+%3C=%28-2x%29%2F-2+%3C4%2F-2+
2+%3E=+x+%3E-2+

or this can also be written -2%3Cx%3C=2
Interval notation is (-2, 2], and the graph on the numberline is all values of x that are BETWEEN -2 and 2, INCLUDING 2 but not -2.

R^2 at SCC