Binomial Theorem

Question
CBSEENMA11014372

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

2 (x – 1) < x + 5,   3 (x + 2) > 2 – x

Solution

space space space 2 left parenthesis straight x minus 1 right parenthesis less than straight x plus 5 space rightwards double arrow space 2 straight x space minus space 2 less than straight x space plus space 5 space rightwards double arrow space 2 straight x space minus straight x less than 5 plus 2 space rightwards double arrow space straight x space less than space 7                         ...(i)
Also,  3 space left parenthesis straight x plus 2 right parenthesis greater than 2 minus straight x rightwards double arrow space 3 straight x plus 6 greater than 2 minus straight x rightwards double arrow 3 straight x plus straight x greater than 2 minus 6 rightwards double arrow 4 straight x greater than negative 4 rightwards double arrow straight x greater than negative 1      ...(ii)

From (i) and (ii), we have -1 < x < 7
The solution set is (-1, 7)
Graphically on number line, we have
                              
                               

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