Question

Solve : $ 2\left( {x - 2} \right) < 3x - 2 $ , $ x \in \{ - 3, - 2, - 1,0,1,2,3\} $ .

Answer 1

Hint: We have to solve the given expression of the inequality and hence state the value of $ x $ which will satisfy the given inequality from the given value of the set of $ x $ . We solve this question using the concept of solving linear equations of inequality . We will first simplify the terms of the inequality by multiplying the terms of the expression . Then we would simplify the expression as in the terms of the expressions in terms of $ x $ , and on further solving the expression of the inequality we will get the range for the value of $ x $ for which it satisfies the given expression . The solution set would be the set which would satisfy the value of the set $ x $ and the condition of inequality .

Complete Step By Step Answer:
Given :
 $ 2\left( {x - 2} \right) < 3x - 2 $ , $ x \in \{ - 3, - 2, - 1,0,1,2,3\} $
Now , we can simplify the expression of the inequality as :
 $ 2x - 4 < 3x - 2 $
Further , we can write the expression as :
 $ - 4 + 2 < 3x - 2x $
 $ - 2 < x $
Hence , we get the expression for $ x $ as :
 $ x > - 2 $
Now , the value of the set $ x $ should satisfy the above condition of the inequality .
So , we get the value of set of $ x $ as :
 $ x \in \{ - 1,0,1,2,3\} $
Hence , the set of the value of $ x $ which satisfies the given conditions of inequality is $ \{ - 1,0,1,2,3\} $ .

Note:
We must take care about the signs and symbols of the inequality , as a slight change causes major errors in the solution . The solution of the range of the inequality states that each and every value which lies in that particular range satisfies the given equation . The round bracket $ \left( {} \right) $ in the value of the range states that the end elements will not satisfy the given expression it is used for the expression with $ < $ or $ > $ greater than or less than symbol whereas the square bracket $ \left[ {} \right] $ states that the end elements of the range will satisfy the given expression it is used for the expression with $ \leqslant $ or $ \geqslant $ greater than equal to or less than equal to symbol .