What this lesson covers
- The step ledger: one row per move, named, applied to both sides
- The probe check that catches a dropped sign in one number
- Fractions: clear them in one row, but the multiplier has to hit every term
- A practice item where all four choices come from real slips
Questions worked in the video
- 0:177(x - 3) = 4x + 9. What is the solution to the given equation?
- 1:37x/3 + 2 = (x - 4)/2. What is the solution to the given equation?
- 2:195(2x + 3) = 8x + 27. What is the solution to the given equation?
Chapters
- 0:00No story to catch your mistake
- 0:17The equation, and four believable answers
- 0:41The step ledger, and two rows that break
- 1:37Fractions: every term, or nothing
- 2:19Your turn
- 2:58Three ways this goes wrong
- 3:18Recap
Lesson transcript
The narration of the video, word for word, under its chapter headings.
0:17The equation, and four believable answers
Here is a display form equation. No story, no units, nothing to sanity check it against. Seven, times the quantity x minus three, equals four x plus nine. Four choices. And every wrong one comes from a real slip.
0:41The step ledger, and two rows that break
Write it as a ledger. One row per move, the move named on the left, applied to both sides. Row one, distribute the seven. Seven x, minus twenty one. Write plus twenty one instead, and here is the catch. Pick any number, say x equals one. The old side gives negative fourteen. The new side gives twenty eight. Different. That row is broken. Fix the sign and the row balances. Negative fourteen, negative fourteen. Row two, take four x off both sides. Three x minus twenty one, equals nine. Row three, add twenty one to both sides. Both sides, not just the left. Three x equals thirty. Row four, divide by three. x equals ten. And ten checks: forty nine on the left, forty nine on the right. The answer is D.
1:37Fractions: every term, or nothing
Fractions look worse and they are not. Multiply both sides by the common denominator and they are gone in one row. x over three, plus two, equals the quantity x minus four, over two. The denominators are three and two, so multiply everything by six. Everything means every term. Six times x over three is two x. Six times two is twelve. Six times the fraction on the right is three x minus twelve. Miss that middle term and the ledger stamps the row broken before the mistake can travel. Finish it, and x is twenty four.
2:19Your turn
Your turn. Five, times the quantity two x plus three, equals eight x plus twenty seven. Ten seconds. Distribute: ten x plus fifteen. Take eight x off both sides, take fifteen off both sides. Two x equals twelve, so x equals six. B. Every other choice is one slip. Negative two left the two x undistributed. Twelve left the three. Twenty one moved the fifteen across with the wrong sign.
2:58Three ways this goes wrong
Three ways this goes wrong. Distributing to the first term and stopping. Moving a term across the equals sign and keeping its sign. And trusting an answer because it appears in the choices. All three die if you write the move on both sides and check the row.
3:18Recap
No story to catch you. So check every row.
Read the written version: the Linear equations · one variable strategy guide, then try 25 hard Linear equations · one variable questions with full explanations. Both are free, no account needed.