SOLVING MODULUS EQ
PAGE 1 OF 5, ONE EQUATION, TWO PATHS
THE SPLIT
ONE INPUT, TWO POSSIBILITIES
Solving a modulus equation means finding every x that makes the absolute value true. The key move is to split one equation into two separate linear paths. Modulus always outputs a size ≥ 0, so the right-hand side must allow that. When you see |x| = k with k > 0, x could be k steps to the right or k steps to the left of zero. That is why one neat equation often hides two answers. Think of it as a fork in the road: follow the plus path, then the minus path, and collect both results.
⚡ CORE RULE
|x| = k with k > 0 gives two cases: x = k or x = −k. Always write both before you stop.
SPLIT!
PLUS PATH
➕ First case: x = k
📍 Point k units right
✅ e.g. |x| = 4 → x = 4
📍 Point k units right
✅ e.g. |x| = 4 → x = 4
MINUS PATH
➖ Second case: x = −k
📍 Point k units left
✅ e.g. |x| = 4 → x = −4
📍 Point k units left
✅ e.g. |x| = 4 → x = −4