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Question
Solve the following inequalities and represent the solution set on a number line:
`3 > (2(3 - 4x))/(7) ≥ - 2`.
Solution
The given inequality `3 > (2(3 - 4x))/(7) ≥ - 2`
which is equivalent to
⇒ 3 x 7 > 2(3 - 4x) ≥ -2 x 7
⇒ `(21)/(2) > 3 - 4x ≥ - 7`
⇒ `-3 + (21)/(2) > -4x ≥ -7 -3`
⇒ `(15)/(2) > -4x ≥ - 10`
we divide this compound inequality by - 4 and reverse the inequality signs to obtain
`(15)/(2 xx (-4)) < x ≤ (-10)/(-4)`
⇒ `(15)/(-8) < x ≤ (5)/(2)`
The graph of this set is `(-15)/(8) < x ≤ (5)/(2)`.
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