Solve the inequality. Graph the solution.
2|x+1/3|<9
2|x + 1/3| < 9
|x + 1/3| < 9/2
-9/2 < x + 1/3 < 9/2
-29/6 < x < 25/6
See
http://www.wolframalpha.com/input/?i=2%7Cx+%2B+1%2F3%7C+%3C+9
To solve the inequality 2|x + 1/3| < 9, we need to isolate the absolute value expression and then solve two separate inequalities.
First, we can divide both sides of the inequality by 2, which gives us |x + 1/3| < 4.5.
Next, we can split the absolute value inequality into two separate inequalities, one for the positive part and one for the negative part:
For the positive part: x + 1/3 < 4.5
Subtracting 1/3 from both sides, we get x < 4.5 - 1/3, which simplifies to x < 4.1667.
For the negative part: -(x + 1/3) < 4.5
Multiplying both sides by -1 (which flips the inequality sign), we get x + 1/3 > -4.5.
Subtracting 1/3 from both sides, we get x > -4.5 - 1/3, which simplifies to x > -4.8333.
So, the solution to the inequality 2|x + 1/3| < 9 is -4.8333 < x < 4.1667.
To graph the solution, we can draw a number line and mark the points -4.8333 and 4.1667 as open circles (since they are not included in the solution). Then, draw a solid line between these two points to represent the range of values that satisfy the inequality.