Posted by jase on .
solve the inequality algebraically. write the solution in interval notation.
the absolute value of x2/3 is less than or equal to 4

precalculus 
Steve,
x  2/3 <= 4
if x  2/3 >= 0 then x  2/3 = x  2/3
In that case,
x  2/3 <= 4
x <= 14/3 and x >= 2/3 (remember x  2/3 >= 0)
so, x is in [2/3 , 14/3]
if x  2/3 >= 0 then x  2/3 = (x  2/3)
In that case,
2/3  x <= 4
x >= 10/3
But x  2/3 < 0 means x < 2/3
So,
x is in [10/3 , 2/3)
So, finally, x is in [10/3 , 2/3)U[2/3 , 14/3]
or, x is in [10/3 , 14/3]
This makes sense. Think of the graph of x. It is a V shape. If x < k, then you want the part of the V below the line y=k.
In this case, the V is shifted 2/3 to the right, and we want the part of the V below the line y=4