|3w+9|=12
1) Let's solve in ℝ: |3w + 9| = 12
Since 12 ≥ 0, |3w + 9| = 12 is equivalent to 3w + 9 = 12 or 3w + 9 = -12
2) Let's solve in ℝ: 3w + 9 = 12
ⓘ We subtract 9 from both sides
3w = 12 -9
ⓘ Start from 12 and move back 9 on the number line: 12 -9 = 3
3w = 3
ⓘ Both sides are divided by 3
w = 33
ⓘ We simplify the fraction by dividing the numerator and the denominator by 3, their greatest common divisor: 33 = 1
Solution obtained: w = 1
3) Let's solve in ℝ: 3w + 9 = -12
ⓘ We subtract 9 from both sides
3w = -12 -9
ⓘ Start from -12 and move back 9 more on the number line, away from zero: -12 -9 = -21
3w = -21
ⓘ Both sides are divided by 3
w = -213
ⓘ We simplify the fraction by dividing the numerator and the denominator by 3, their greatest common divisor: -213 = -7
Solution obtained: w = -7
▶Solution:   w = { -7, 1 }