Binomial Theorem

Question
CBSEENMA11014370

Solve the following inequality and represent the solution graphically on the number line. 

5 (2x – 7) – 3 (2x + 3) ≤ 0 ,   space space 2 straight x plus 19 space less or equal than space 6 straight x plus 47.


Solution

5 (2x – 7) – 3 (2x + 3) ≤ 0 
rightwards double arrow     10 straight x minus 35 minus 6 straight x minus 9 space less or equal than space 0 space rightwards double arrow space 10 straight x minus 6 straight x less or equal than 9 plus 35 space rightwards double arrow space 4 straight x less or equal than 44 space rightwards double arrow space straight x less or equal than 11            ...(i)
Also,           2 straight x plus 19 less or equal than 6 straight x plus 47
rightwards double arrow           2 straight x minus 6 straight x space less or equal than space 47 minus 19 space rightwards double arrow space minus 4 straight x less or equal than space 28 space rightwards double arrow space fraction numerator negative 4 straight x over denominator negative 4 end fraction greater or equal than fraction numerator 28 over denominator negative 4 end fraction space rightwards double arrow space straight x space greater or equal than space minus 7             ...(ii)
From (i) and (ii), we have space space minus 7 less or equal than straight x less or equal than 11
∴   The solution set is [-7, 11]. Graphically, we have
           

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