Whatever you do to one side of the =, do the exact same thing to the other side. That's why we write +3w or ÷5 under BOTH sides — the equation stays balanced, like a scale.
Parentheses → Exponents → Multiply & Divide (left to right) → Add & Subtract (left to right).
3w means 3 × w — the multiplication is "glued" to the w tighter than any + or −. So in 3w + 2, the 3 and the w are one package; the +2 is separate.
To free the w, peel the layers off backwards: first undo the + and − (move the plain numbers away), and only THEN undo the × and ÷ (divide by the number on the w). That's why we move the −7/4 across before we divide.
Only terms with the same letter part can combine. 5w − 2w = 3w ✓. But 2 − 3w? The 2 has no w — NOT like terms, they can never combine.
Really it's the Golden Rule in disguise: add 3w to both sides, and the −3w disappears on one side while +3w appears on the other. Minus becomes plus. Every single time.
w + 3w = 4w, because the lonely w is really 1w.
• Add or subtract fractions only when the bottoms match (a whole w = 4w/4).
• Dividing by a fraction = multiplying by its flip (÷ 3/4 is × 4/3).
• Two EQUAL fractions? Cross-multiply the diagonals — it's really multiplying both sides by both bottoms at once.
• A fraction like 2/7 is a perfectly good final answer!