Binomial Theorem

Question
CBSEENMA11014367

Solve the following inequality and show the graph of the solution on the number line.

3 (1 - x) < 2 (x + 4)

Solution

3 (1 - x) < 2 (x + 4)
rightwards double arrow          3 minus 3 x less than 2 x plus space 8 space rightwards double arrow space minus 3 x minus 2 x space less than space 8 minus 3 space rightwards double arrow negative 5 x less than 5
rightwards double arrow                fraction numerator negative 5 straight x over denominator negative 5 end fraction greater than fraction numerator 5 over denominator negative 5 end fraction                                                (∵ -5 < 0)
rightwards double arrow                     x > - 1
Hence, the solution of the inequality is left parenthesis negative 1 comma space infinity right parenthesis
Graph on the number line is:
                    

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