Binomial Theorem

Question
CBSEENMA11014371

Solve the following pair of inequality and represent the solution graphically on the number line:

 3x – 7 > 2 (x – 6) , 6 – x > 11 – 2x

Solution

3 straight x minus 7 space greater than 2 space left parenthesis straight x minus 6 right parenthesis space rightwards double arrow space 3 straight x minus 7 space greater than 2 straight x minus 12 space rightwards double arrow space 3 straight x minus 2 straight x greater than negative 12 plus 7
rightwards double arrow                 x> - 5                                                                                             ...(i)

Also,             6 minus straight x greater than 11 minus 2 straight x rightwards double arrow space minus straight x space plus space 2 straight x greater than 11 minus 6 rightwards double arrow straight x greater than 5                                 ...(ii)
From (i) and (ii), we have space space straight x greater than 5 space rightwards double arrow space straight x space element of space left parenthesis 5 comma space infinity right parenthesis
The solution set is space space left parenthesis 5 comma space infinity right parenthesis. Graphically on number line, we have
                 

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