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Question
Find the values of x, which satify the inequation
-2`5/6 < 1/2 - (2"x")/3 ≤ 2, "x" in "W"`
Graph the solution set on the number line.
Solution
We need to find the values of x, such that
x satisfies the inequation -2`5/6 < 1/2 - (2"x")/3 ≤ 2, "x" in "W"`
Consider the given inequation:
-2`5/6 < 1/2 - (2"x")/3 ≤ 2`
⇒ `-17/6 < (3-4"x")/6 ≤ 12/6`
⇒ `-17/6 < (4"x"-3)/6 ≤ 12/6`
⇒ 17 > 4x - 3 ≥ -12
⇒ -12 ≤ 4x -3 < 17
⇒ -12 + 3 ≤ 4x - 3 + 3 < 17 + 3
⇒ -9 ≤ 4x < 20
⇒ `-9/4 ≤ (4"x")/4 < 20/4`
⇒ `-9/4 ≤ x < 5
Since `"x" in "W"` the value of x are 0,1,2,3,4.
And the required line is
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