SOLUTION: Solve the inequality. Express your answer using set notation and interval notation. Graph the solution set. (1/3) < [(x + 1)/2] <= (2/3)

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Question 1208859: Solve the inequality. Express your answer using set notation and interval notation. Graph the solution set.

(1/3) < [(x + 1)/2] <= (2/3)




Answer by math_tutor2020(3817) About Me  (Show Source):
You can put this solution on YOUR website!

1%2F3+%3C+%28x%2B1%29%2F2+%3C=+2%2F3

2%2A%281%2F3%29+%3C+2%2A%28x%2B1%29%2F2+%3C=+2%2A%282%2F3%29 Multiply all sides by 2

2%2F3+%3C+x%2B1+%3C=+4%2F3

2%2F3+-+1+%3C+x%2B1-1+%3C=+4%2F3+-+1 Subtract 1 from all sides

2%2F3+-+3%2F3+%3C+x+%3C=+4%2F3+-+3%2F3

-1%2F3+%3C+x+%3C=+1%2F3

The answer in set builder notation would be
That translates to "x is any real number between -1/3 and 1/3; excluding -1/3 but including 1/3".

The interval notation would be (-1/3, 1/3]
A curved parenthesis means we exclude the endpoint -1/3.
A square bracket is there to include the endpoint 1/3.

Here's the graph on a number line.

Described in words: plot an open hole at -1/3 and a closed filled in circle at 1/3. Shade in between.

Another way to express the diagram could be like this
              -1/3     1/3
--|--------|-----O==|==●-----|--------|--
 -2       -1        0        1        2