How do you solve absolute value inequalities with absolute value variables on both sides #abs(2x)<=abs(x-3)#?
All values of x in the interval [-3,2]
To remove the absolute value sign, square both sides, so that both would be positive only. Accordingly,
Now, there can be two options for this inequality to hold good.
Case 1 x+3 is positive, that is x
Case 2 x+3 is negative, that is x
To understand the solution mark the above inequalities on the number line. The solution to the inequality would be x