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1
What You'll Master
objectives
Know
Two-step equations require two inverse operations applied in reverse order
The structure of an equation of the form $ax + b = c$
Understand
Undo operations using SADMEP (the reverse of BEDMAS) — undo $+/-$ first, then $\times/\div$
Why the order of undoing matters
Can Do
Solve equations of the form $ax + b = c$ in two clear steps
Check answers by substituting back into the original equation
2
Words You Need
vocabulary
Two-Step EquationAn equation that requires exactly two inverse operations to isolate the variable. e.g. $3x + 7 = 19$.
Reverse OrderWhen solving, you undo operations in the opposite order to how they were applied. Last operation done is the first undone.
SADMEPSubtract/Add first, then Divide/Multiply — the reverse of BEDMAS. The order for undoing operations when solving equations.
CoefficientThe number multiplying the variable. In $3x$, the coefficient is 3. You undo this by dividing in the second step.
ConstantA fixed number added or subtracted in the equation, like the $+7$ in $3x + 7 = 19$. You undo this in the first step.
3
Reverse Order Undoing
+5 XP
To solve $ax + b = c$, you undo the operations in reverse order — the last operation applied is the first one you undo.
Think of it like getting dressed: you put your socks on before shoes, so you take your shoes off before socks. In $3x + 7$, the variable is first multiplied by 3, then 7 is added. To undo: first subtract 7, then divide by 3.
$$ax + b = c \;\xrightarrow{-b}\; ax = c-b \;\xrightarrow{\div a}\; x = \frac{c-b}{a}$$
Step 1: Undo $+$ or $-$
Subtract the constant if it's added; add it if it's subtracted. Do this to both sides.
Step 2: Undo $\times$ or $\div$
Divide by the coefficient if the variable is multiplied; multiply if it's divided.
SADMEP rule
S-A first, then D-M. Subtract/Add before Divide/Multiply — the reverse of BEDMAS.
4
Worked Method — Two Full Examples
+5 XP
Watch each example. Every step is labelled so you know exactly why each move is made.
Example 1 — $3x + 7 = 19$
Working
Why?
$3x + 7 = 19$
Start with the equation.
$3x + 7 - 7 = 19 - 7$
Step 1: subtract 7 from both sides (undo the $+7$).
$3x = 12$
Simplify.
$3x \div 3 = 12 \div 3$
Step 2: divide both sides by 3 (undo the $\times 3$).
$x = 4$
Solution found.
Check: $3(4) + 7 = 12 + 7 = 19$ ✓
Substituting back confirms $x = 4$.
Example 2 — $2x - 5 = 11$
Working
Why?
$2x - 5 = 11$
Start with the equation.
$2x - 5 + 5 = 11 + 5$
Step 1: add 5 to both sides (undo the $-5$).
$2x = 16$
Simplify.
$2x \div 2 = 16 \div 2$
Step 2: divide both sides by 2 (undo the $\times 2$).
$x = 8$
Solution found.
Check: $2(8) - 5 = 16 - 5 = 11$ ✓
Substituting back confirms $x = 8$.
5
Word Problems to Equations
+5 XP
Real-world problems can be turned into two-step equations. The key is to identify the unknown, translate the words into algebra, then solve.
Problem: A taxi charges $2 per km plus a $5 flag fall. A trip costs $27 in total. How far did the taxi travel?
Let $d$ = distance in km. The equation is: $$2d + 5 = 27$$
Subtract 5: $2d = 22$. Divide by 2: $d = 11$ km.
$2(11) + 5 = 22 + 5 = 27$ ✓
Name the unknown
Start every word problem by writing "Let $x$ = ..." with a clear description.
Per means $\times$
"$2 per km" means $2d$. Rate words like "per", "each", "for every" become multiplication.
Fixed fee means $+$
A one-off charge like "flag fall" or "joining fee" becomes the constant term in your equation.
Watch Me Solve It · Worked example
Watch Me Solve It — $5x - 3 = 22$
+15 XP per step
Q
PROBLEM
Solve $5x - 3 = 22$. Show all working and check your answer.
The coefficient is 5. Dividing both sides by 5 undoes the multiplication and gives us $x$ on its own.
3
Check by substituting $x = 5$
$5(5) - 3 = 25 - 3 = 22$ ✓
Always check! Substitute your answer back into the original equation. Both sides equal 22, so $x = 5$ is correct.
Nice work — XP earned
Answer$x = 5$
6
Common Pitfalls
heads-up
Dividing before undoing the constant
In $3x + 7 = 19$, a common error is to divide by 3 first, giving $x + 7 = \frac{19}{3}$ — which creates messy fractions and the wrong answer.
Fix: always undo $+/-$ first (SADMEP). Subtract 7 to get $3x = 12$, then divide by 3 to get $x = 4$.
Forgetting to apply the operation to BOTH sides
Writing $3x + 7 - 7 = 19$ (only subtracting from the left side) breaks the balance of the equation and gives an incorrect result.
Fix: treat the equation like a balanced scale. Whatever you do to one side, you must do to the other. Write it out: $3x + 7 - 7 = 19 - 7$.
Not checking the answer
Skipping the check step means you won't catch arithmetic errors. You might write $x = 6$ when the correct answer is $x = 4$.
Fix: always substitute your answer back into the original equation. If both sides are equal, you're correct. If not, find the error.
Quick Check · 5 questions
1
Solve $3x + 4 = 19$.
+10 XP
2
What is the FIRST step to solve $5x - 8 = 27$?
+10 XP
3
Solve $\frac{x}{6} - 3 = 4$.
+10 XP
4
"A taxi charges a $5 flag fall plus $2 per kilometre. A trip costs $27." Which equation finds the distance $d$?
+10 XP
5
Solve $4x + 2.5 = 18.5$.
+10 XP
ApplyEasy2 MARKS
Q1. Solve $7x - 9 = 26$. Show each step clearly and check your answer.
Answer in your workbook.
ApplyMedium3 MARKS
Q2. Solve $\frac{x}{3} + 8 = 5$. Show each step and check your answer.
Answer in your workbook.
ApplyHard4 MARKS
Q3. A gym membership costs a $25 joining fee plus $15 per week. If Maria paid $175 in total for her first period, write and solve an equation to find how many weeks she attended.
Answer in your workbook.
Stretch Challenge · +25 XP, +10 coins
Extension Problems
Ready for a bigger challenge? Try these extension problems.
R
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Key Concept
Review the main ideas from this lesson.
Formulas
Key formulas and rules.
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Common mistakes to avoid.
Check
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