abs(x)=x
1) Let's solve in ℝ: abs(x) = x
The absolute-value arguments are zero at 0. Split ℝ at these points and solve on each interval
On (-∞, 0]: x ≤ 0, so abs(x) = -x
On (-∞, 0], the equation becomes -x = x
2) Let's solve in ℝ: -x = x
-x -x = 0
ⓘ Like terms are grouped by adding their coefficients: -x -x = -2x
-2x = 0
We simplify the expression by -2
⇥Let's solve in ℝ: x = 0
⇥Solution found: x = 0
As 0 ≤ 0, we can keep the solution 0
On [0, +∞): x ≥ 0, so abs(x) = x
On [0, +∞), the equation becomes x = x
3) Let's solve in ℝ: x = x
x -x = 0
ⓘ Like terms are grouped by adding their coefficients: x -x = 0
0 = 0
Solution found: x ∈ ℝ
The equation holds for every x in [0, +∞): keep the whole interval
▶Solution found: x ≥ 0