Lesson Guide
Explanation
In 3x + 4 = 19 there are two things attached to x: it has been multiplied by 3, and then 4 has been added. Two operations means two steps to undo them. The order matters, and the way to remember it is socks and shoes — x put on the multiplication first and the addition second, so to undo it you take the addition off first. Undo the +4 before the ×3.
Your Turn
For 5x − 2 = 13, name the two things done to x and which you would undo first. Check: multiplied by 5 then 2 subtracted; undo the subtraction first.
Watch Out
Undoing in the same order as the equation is the classic error. Reverse the order.
Explanation
Step one: get rid of the loose number. Subtract 4 from both sides and 3x + 4 = 19 becomes 3x = 15. Look at what has happened — that is a one-step equation, exactly the kind you solved in the last lesson. This is the whole trick with two-step equations: one move reduces them to something you can already do. There is genuinely nothing new here, just one extra line of working.
Your Turn
Take the first step on 2x + 7 = 19 without finishing. Check: subtract 7 from both sides, leaving 2x = 12.
Watch Out
Do not touch the 3 in 3x yet. Deal with the loose number first, then the multiplier.
Explanation
Step two finishes it. 3x = 15, so divide both sides by 3 and x = 5. Then check in the original equation, not in a line of your working — if you made a mistake at step one, checking against your own error would not catch it. Substituting: 3 times 5 is 15, plus 4 is 19. Correct. Notice the check uses order of operations, multiplying before adding, exactly as it should.
Your Turn
Finish 2x = 12 and check it in 2x + 7 = 19. Check: x = 6, and 2 × 6 + 7 = 19.
Watch Out
Check in the ORIGINAL equation. Checking your own working line will confirm a mistake instead of catching it.
Explanation
When the loose number is subtracted, the same rule applies but it feels wrong at first. In 4x − 5 = 23, five is being taken away from 4x, so you put it back by adding 5 to both sides. That gives 4x = 28, then divide by 4 for x = 7. The minus sign sitting there tempts you to subtract, and that is exactly the trap from the last lesson showing up again in a bigger equation. Do the opposite of what you see.
Your Turn
Solve 3n − 8 = 7. Check: add 8 to get 3n = 15, then divide by 3 for n = 5.
Watch Out
4x − 5 = 23 needs +5, not −5. Subtracting gives 4x = 18 and a wrong answer.
Explanation
This is where equations start earning their keep. Tickets cost $8 each with a $6 booking fee, and the total was $54 — how many tickets? Start by saying what the letter stands for: let t be the number of tickets. Then the cost is 8t + 6, and that equals 54. Solve it in the two steps you now know and t = 6. Two habits matter here: always say what your letter means before you use it, and always finish by answering the actual question in words — six tickets, not just t = 6.
Your Turn
A taxi charges $4 flagfall plus $2 per km. The fare was $18. Write an equation and solve for the distance. Check: 2d + 4 = 18, so d = 7 km.
Watch Out
Do not stop at t = 6. The question asked how many tickets, so answer it: 6 tickets.
📌 Key Points — this lesson in a nutshell
- Two operations on x means two steps to undo them.
- Undo in reverse order: the loose number first, the multiplier second.
- Step one turns it into a one-step equation you already know.
- A subtracted number is cleared by adding, however wrong that feels.
- Check in the original equation, never in your own working.
- For word problems, say what the letter means and answer in words.
Step 1: Introduction
Step 1 of 5
Was this lesson helpful? Rate this Course
Discussion
Loading comments...