What this lesson covers
- Pin the target: the asked-for expression goes on the board before you solve
- Why x = 6 sitting in the choices is a designed trap, not a coincidence
- The one-move shortcut when the target is a multiple of the whole equation
- A practice problem with the clock running, and the two-second check that closes the category
Questions worked in the video
- 0:17If 4 − 2x = 3x − 26, what is the value of 3x?
- 1:55If 6x + 9 = 51, what is the value of 2x + 3?
- 2:33If 8x − 5 = 3x + 35, what is the value of 4x?
Chapters
- 0:00They asked for 3x, not x
- 0:17The setup
- 0:53Solve, then build the target
- 1:55When you never need x
- 2:33Your turn
- 3:07Three ways this goes wrong
- 3:29Solve for x, then answer what they asked
Lesson transcript
The narration of the video, word for word, under its chapter headings.
0:17The setup
Straight algebra. No story, no units. 4 minus 2x equals 3x minus 26. Now read the last four words of the question. What is the value of 3x. Not x. 3x. Pin that on the wall before you touch the equation. The algebra here is easy, and that is deliberate. The difficulty lives in the last line, not in the solve. Three of these four choices are numbers you will genuinely produce on the way. So the target goes up on the board first, and it stays there until something fills it.
0:53Solve, then build the target
Collect the x terms on one side and the numbers on the other. Add 2x to both sides. Add 26 to both sides. That gives 5x equals 30. Divide by 5, and x equals 6. And here is the moment the whole question is built around. You are finished solving, and you have not answered anything yet. Now look at what is sitting in the choices. 6 is x. 30 is 5x, the line right before you divided. Negative 6 is what one dropped sign hands you. Every single one of them is a correct answer to a question nobody asked. 3 times 6 is 18. That is the only one that fills the target. Same equation, different target. If the question had asked for x plus 4 instead, every line of that solve would be identical. Only the last step changes. 6 plus 4 is 10. The solve does not care what they asked for. You do.
1:55When you never need x
Sometimes you never need x at all. 6x plus 9 equals 51, and the target is 2x plus 3. Look at the left side. Every term is exactly 3 times the target. So divide the whole equation by 3. 2x plus 3 equals 17. One move, and x never appeared. One habit closes this whole category. After you circle an answer, read the question one more time, and check that the thing you circled has the same name as the thing they asked for. It costs about two seconds.
2:33Your turn
Your turn. 8x minus 5 equals 3x plus 35. They want 4x. Ten seconds. 5x equals 40, so x equals 8. Do not stop there. 4x is 32. C. 8 is x. 40 is 5x. And negative 8 is the dropped sign. Same shape as before. The intermediate, the sign slip, and x itself, all sitting in the choices, all waiting.
3:07Three ways this goes wrong
Three ways this goes wrong. Solving perfectly, then circling x out of habit. Stopping one line early and picking the intermediate. And assuming the target is always x, when sometimes you can build it straight off the equation. All three are really the same mistake. Answering a question that was never asked.
3:29Solve for x, then answer what they asked
Solve for x. Then answer the question they actually asked.
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.