sandal85 wrote:

Which values of x are solutions to the inequality |x + 1| + |x - 1| <= 2 ?

Apart from algebra can we think conceptually to solve this

You can solve this question using the number line approach too.

"Distance of x from -1" + "Distance of x from 1" <= 2

----------(-2)-----(-1)-----0-----(1)-----(2)--------

Note that distance between -1 and 1 is 2 so whenever x is between these two values, the sum of distance from -1 and 1 will be 2

----------(-2)-----(-1)---x--0-----(1)-----(2)--------

Hence all values between -1 and 1 (inclusive) will satisfy this condition.

When you go to the right of 1 or left of -1, the sum of distances from -1 and 1 will exceed 2. So the only range that satisfies the inequality is

-1 <= x <= 1

thanks a ton! that's pretty much clear. It would be great if you explain the range of values that satisfy |x+3| - |4-x| = |8+x| in the same method....