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A quick, calm intro — then you choose when to climb.
An equation is a scale in perfect balance: the two sides weigh the same. Do the same thing to both sides and the balance holds — that one rule lets you free x and read its value.
Every step explained — why we do it, and what happens.
Why: Read it as a balanced scale: the unknown x plus 4 weighs exactly the same as 12.
What happens: Our mission: get x alone on one side. The +4 is the only thing in the way.
Why: To free x we undo the "+ 4". The balance rule says: subtract 4 from BOTH sides so the scale stays level.
What happens: Both sides lose 4 — the scale is still balanced, so the equation is still true.
The +4 and −4 cancel each other on the left, leaving x alone.
12 − 4 = 8 — that is the answer.
Why: The check: put x = 8 back into the ORIGINAL equation to see if the scale balances.
What happens: 8 + 4 = 12 and the other side is 12 — 12 = 12, so x = 8 is right.
A sunflower seedling is already 20 cm tall, and it grows 7 cm every week. After how many weeks will it reach 62 cm? Let w be the number of weeks: the height is 20 (the start) + 7 × w (the growth).
Why: Translate the story into math: start + growth × weeks = final height.
What happens: The story becomes an equation — a scale we can solve.
Why: Undo the "+ 20" first — the starting height is known, so we remove it from both sides.
What happens: Both sides drop by 20; the balance holds.
20 − 20 = 0, so only 7w is left; 62 − 20 = 42.
Why: w is multiplied by 7, so we undo with division — divide BOTH sides by 7.
What happens: The left becomes just w; the scale is still level.
42 ÷ 7 = 6 — six weeks.
Why: Check: after 6 weeks the height should be 62 cm.
What happens: 20 + 42 = 62 ✓ — the sunflower reaches 62 cm after exactly 6 weeks.
Two classic glitches:
1.Subtracting from only one side
Wrong: — the scale tips, the answer goes wrong
Right:Do the same to both sides: .
2.Undoing in the wrong order
Wrong:Dividing before removing the constant
Right:Undo first, then .
You've got the concept! Let's lock it in with practice.
Learning is optional — the ladder is always open.