the maximum no of values of x if|x-2|+|x-4|=2 is Share with your friends Share 0 Tanveer Sofi answered this We are given thatx-2+x-4=2Now, consider the interval of real numbers, for which the given equation assumesdifferent forms:when x<2, we have x-2=-x-2 and x-4=-x-4. The equation can be written as:-x-2-x-4=2⇒-2x+6=2⇒-2x=-4⇒x=2But, x<2, thus x=2 is not a solution.When, 2≤x<4, we have x-2=x-2 and x-4=-x-4The equation can be written as:x-2-x-4=2⇒-2+4=2⇒2=2Which is an identity, therefore for interval [2,4), the equation is always true.When , x≥4, we have x-2=x-2 and x-4=x-4.The equation can be written asx-2+x-4=2⇒2x-6=2⇒2x=8⇒x=4Then, x=4 is the solution of the equation.Therefore, the above equation is true only in the interval [2,4].If x is an integer, than the maximum possible values of x are 3, i.e. x=2,3,4. 11 View Full Answer Aryan answered this The maximum number of values is 3. And these values are 2,3,4 6
