Example 1:     Solve:  | x | = 4 

• Enter left side in f1(x).  Enter right side in f2(x).
  You can find abs( ) under the template button

  

• Use the Intersect Option: #6 Analyze Graph, #4 Intersection.
  Use this option twice to find the two points of intersection. The x-values are the solutions.

• Answer:  x = 4;  x = -4

  
  

 

• Answer:  x = 2;  x = 3.33
  (The 3.33 is repeating. 3.3333333333.)
  To convert to a fraction:
  Type 3.333333333333
  , #2, #2,
  
  Answer:  x = 2;  x = 10/3
  
  

 

• Answer:  x = -0.4;  x = 2

Example 4:    Solve: | 2 - x | = 5

Scratchpad: :

, #3 Algebra, #1 Numerical Solve
or just type nSolve(

Type in your equation, followed by the variable.
nSolve( | 2 - x | = 5, x)

WHOA!!

The TI-Nspire CS II non-CAS treats absolute value as a numerical piecewise function (in parts), giving one answer (which is the answer closest to the origin).
You will need to state approximately where you want to look for each answer. Simplify this process by starting with one positive interval and one negative interval. If each yields a solution, you are done. If one gives no solution, go back to the other interval and narrow in on the choice. If you have "no idea" where the answer might be, just set a larger positive interval and larger negative interval. You will need to check BOTH possibilities (and perhaps even more) to find the answers.

nSolve ( | 2 - x | = 5, x, 0, 10 ) for a positive solution.

nSolve ( | 2 - x | = 5, -10, 0 ) for a negative solution.

Answer:   x = -3, x = 7

Whoa!!!
Isn't there another answer?
Check the graph.

Yep! There is another answer.
How do I get it to show up in nSolve?


If you do not set an interval, the calculator will
pick the answer closest to the origin.

That "Using Graph" method
is looking better and better.