|x-3|+3=7
Let's solve in ℝ: |x -3| + 3 = 7
ⓘ We subtract 3 from both sides
|x -3| = 7 -3
ⓘ Start from 7 and move back 3 on the number line: 7 -3 = 4
|x -3| = 4
Since 4 ≥ 0, |x -3| = 4 is equivalent to x -3 = 4 or x -3 = -4
Let's solve in ℝ: x -3 = 4
ⓘ We add 3 to both sides
x = 4 + 3
ⓘ Start from 4 and move forward 3 on the number line: 4 + 3 = 7
Solution obtained: x = 7
Let's solve in ℝ: x -3 = -4
ⓘ We add 3 to both sides
x = -4 + 3
ⓘ Start from -4 and move forward 3 on the number line, getting closer to zero: -4 + 3 = -1
Solution found: x = -1
▶Solution:   x = { -1, 7 }