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 $⩽$ or $⩾$ greater than equal to or less than equal to symbol .