Question

How do you solve `abs(5-x)<=x`?

Answer 1

Use the piecewise definition of the absolute value function, `|f(x)|={(f(x);f(x)>=0),(-f(x);f(x)<0):}` to separate into two inequalities.
Solve both inequalities.

Explanation:

Separate into two inequalities:

`5-x <=x` and `-(5-x) <= x`

Distribute the minus sign in the second inequality:

`5-x <=x` and `-5+x <= x`

Add x to both sides of the first inequality and subtract x from both sides of the second:

`5 <=2x` and `-5 <= 0`

The second inequality does not depend on x, therefore, we discard it.

Divide both sides of the first inequality by 2:

`5/2 <=x`

Flip the inequality

`x >= 5/2`