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Question
Solve the following inequation and represent the solution set on a number line.
`-8 1/2 < -1/2 -4x <= 7 1/2`, x ∈ 1
Solution
`-81/2 < -1/2-4x<=71/2`, x ∈ I
`=> -17/2 < -1/2 - 4x <= 15/2`, x ∈ I
Take `-17/2 < -1/2 - 4x` `-1/2 - 4x <= 15/2`
`-17/2 + 1/2 < -4x` `-4x <= 15/2 + 1/2`
`-16/2 < -4x` `-4x <= 16/2`
-8 < -4x `-4x <= 8`
2 > x `x >= -2`
Thus, on simplifying, the given inequation reduces to -2 ≤ x 2.
Since x ∈ I, the solution set is { -2, -1, 0, 1}.
The required graph on the number line is as follows:
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