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Question

Mathematics Question on inequalities

Solve the inequality −12<4−3x−5≤2 -12 < 4-\frac{3x}{-5} ≤ 2.

Answer

−12<4−3x−5≤2 -12 < 4-\frac{3x}{-5} ≤ 2
⇒−12−4<−3x−5≤2−4⇒ -12-4 < \frac{-3x}{-5} ≤ 2-4
⇒−16<−3x−5≤−2⇒ -16 < \frac{-3x}{-5} ≤ -2
⇒ -80 < 3x ≤ -10
⇒−803<3≤−103⇒ \frac{-80}{3} < 3 ≤ \frac{-10}{3}
Thus, the solution set for the given inequality is (−803,−103].(\frac{-80}{3}, \frac{-10}{3}].