Before diving into the practice questions, take a moment to think about what you already know about this topic.
Record in workbook.
1
What You'll Master
objectives
Know
The inverse of addition is subtraction (and vice versa)
Understand
To solve an equation, undo the operation using its inverse — applied to both sides
Can Do
Solve equations of the form $x + a = b$
Solve equations of the form $x - a = b$
2
Words You Need
vocabulary
Inverse OperationAn operation that undoes another. Addition and subtraction are inverses of each other.
UndoTo reverse an operation. We undo $+5$ by doing $-5$, and undo $-3$ by doing $+3$.
BalanceBoth sides of an equation are equal — like a balanced scale. Any operation applied to one side must be applied to the other.
Additive InverseThe number you add to get zero. The additive inverse of $5$ is $-5$; of $-3$ is $+3$.
SolveTo find the value of the unknown that makes the equation true.
3
Inverse Operations
+5 XP to read
Addition and subtraction are inverse operations — they undo each other. This is the key to solving equations.
To isolate $x$, apply the inverse operation to both sides of the equation. Think of the equation as a balanced scale — whatever you do to one side, you must do to the other to keep it balanced.
$+5$ undone by $-5$
$+5$ undone by $-5$
$x + 5 - 5 = x$. Adding then subtracting the same number gets you back to $x$.
$-3$ undone by $+3$
$x - 3 + 3 = x$. Subtracting then adding the same number returns to $x$.
The golden rule
Whatever is added to $x$ — subtract it from both sides to isolate $x$.
4
Solving $x + a = b$
+5 XP
Method: subtract $a$ from both sides to isolate $x$.
When $x$ has something added to it, use subtraction to undo it. Apply the same subtraction to both sides to keep the equation balanced.
$x - 12 = -5$
Add 12 to both sides: $x = -5 + 12 = 7$
Watch Me Solve It · Worked examples
Watch Me Solve It · Two worked examples
+15 XP per step
Example A
Q
PROBLEM
Solve $x + 6 = 14$
1
Identify the operation on $x$
$x$ has $+6$ added to it
The inverse of $+6$ is $-6$.
2
Subtract 6 from both sides
$x + 6 - 6 = 14 - 6$
Apply the inverse operation to both sides.
3
Simplify
$x = 8$
Left side: $x + 0 = x$. Right side: $14 - 6 = 8$.
4
Check your answer
$8 + 6 = 14$ ✓
Substitute $x = 8$ back in. Both sides equal 14.
Answer$x = 8$
Example B
Q
PROBLEM
Solve $x - 9 = 3$
1
Identify the operation on $x$
$x$ has $9$ subtracted from it
The inverse of $-9$ is $+9$.
2
Add 9 to both sides
$x - 9 + 9 = 3 + 9$
Apply the inverse operation to both sides.
3
Simplify
$x = 12$
Left side: $x + 0 = x$. Right side: $3 + 9 = 12$.
4
Check your answer
$12 - 9 = 3$ ✓
Substitute $x = 12$ back in. Both sides equal 3.
Answer$x = 12$
XP earned
6
Common Pitfalls
heads-up
Subtracting from one side only
Writing $x + 6 = 14 \Rightarrow x = 14$ (forgot to subtract 6 from the right side) breaks the balance. Both sides must stay equal.
Fix: always apply the inverse operation to both sides. $x + 6 - 6 = 14 - 6 \Rightarrow x = 8$.
Confusing the direction
Seeing $x + 6 = 14$ and adding 6 instead of subtracting it. If the equation shows $+6$, you subtract 6 from both sides — not add it.
Fix: ask "what is being done to $x$?" then do the opposite to both sides.
Forgetting to check
Skipping the verification step means a simple arithmetic slip can go unnoticed. Always substitute your answer back into the original equation.
Fix: for $x = 8$ from $x + 6 = 14$, check: $8 + 6 = 14$ ✓. If it doesn't balance, re-examine your working.
Quick Check · 5 questions
1
Solve $x + 9 = 14$.
+10 XP
2
Solve $x - 7 = 3$.
+10 XP
3
Solve $5 = x + 12$.
+10 XP
4
"A number increased by 6.5 equals 10." Which equation and solution are correct?
+10 XP
5
Which inverse operation solves $x - 2.8 = 5.4$?
+10 XP
ApplyEasy2 MARKS
Q1. Solve $x + 11 = 7$. Show your working and check your answer.
Answer in your workbook.
ApplyMedium3 MARKS
Q2. Solve $x - 3.6 = 8.9$. Show your working and check your answer.
Answer in your workbook.
ApplyHard4 MARKS
Q3. A recipe needs 250g of flour. After adding some flour to a bowl, the chef adds another 75g and now has exactly 250g. Write an equation and solve to find how much flour was in the bowl to start with.
Answer in your workbook.
Stretch Challenge · +25 XP, +10 coins
Extension Problems
Ready for a bigger challenge? Try these extension problems.
R
Quick Review
Key Concept
Review the main ideas from this lesson.
Formulas
Key formulas and rules.
Watch Out
Common mistakes to avoid.
Check
Always verify your answers.
Practice
Keep practicing to master.
Next
Build on these skills.
Interactive: Algebra Machine
Substitute numbers into algebraic expressions and see them evaluate step by step.
Your Badges
0 of 6
First Steps
3-Day Streak
3 in a Row
Lesson Ace
Stretch Seeker
Daily Warrior
Mark lesson as complete
Tick when you've finished Learn, Practice and the Stretch. Earns +90 XP and +25 coins.