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Question
Find the values of x, which satisfy the inequation `-2 5/6 < 1/2 - (2x)/3 ≤ 2, x ∈ W`. Graph the solution set on the number line.
Solution
Consider the given inequation:
`-2 5/6 < 1/2 - (2x)/3 ≤ 2`
`=> (-17)/6 < (3 - 4x)/6 < 12/6`
`=> 17/6 > (4x - 3)/6 ≥ (-12)/6`
`=> 17 > 4x - 3 ≥ -12`
`=> -12 ≤ 4x - 3 < 17`
`=> -12 + 3 ≤ 4x - 3 + 3 < 17 + 3`
`=> -9 ≤ 4x < 20`
`=> -9/4 ≤ (4x)/4 < 20/4`
`=> -9/4 ≤ x < 5`
Since x ∈ W, the required solution set = {0, 1 ,2, 3, 4}
And the required number line is as follows:
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