Before diving into the practice questions, take a moment to think about what you already know about this topic.
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1
What You'll Master
objectives
Know
The difference between an expression and an equation
Understand
The equals sign represents balance — both sides must stay equal
Can Do
Determine whether a value is a solution by substitution
2
Words You Need
vocabulary
EquationA maths sentence that says two things are equal, always containing an equals sign. e.g. $3x + 5 = 14$.
LHS (Left-Hand Side)Everything to the left of the equals sign. In $3x + 5 = 14$, the LHS is $3x + 5$.
RHS (Right-Hand Side)Everything to the right of the equals sign. In $3x + 5 = 14$, the RHS is $14$.
SolutionThe value of the variable that makes an equation true (LHS = RHS).
SubstitutionReplacing a variable with a number to check whether it satisfies the equation.
Balancing PrincipleWhatever you do to one side of an equation, you must do the same to the other side to keep it equal.
3
Expressions vs Equations
+5 XP
The single most important distinction in beginning algebra is the equals sign.
Expression — no equals sign
$3x + 5$ is just a phrase. It has no equals sign, so nothing is being claimed — it cannot be "solved".
Equation — has an equals sign
$3x + 5 = 14$ is a complete sentence. The equals sign claims the two sides are balanced.
The Solution
The value of $x$ that makes the equation true is called the solution. For $3x + 5 = 14$, the solution is $x = 3$.
Think of an equation like a complete sentence. An expression like $3x + 5$ is just a phrase — it says something, but makes no claim. An equation like $3x + 5 = 14$ is a sentence — it claims the left side equals the right side. Your job is to find the value of $x$ that makes the claim true.
$3x + 5 = 14$
Quick check: Which has an equals sign — $2x + 7$ or $2x + 7 = 11$?
Answer: $2x + 7 = 11$ has an equals sign, so it is an equation. $2x + 7$ is an expression.
4
The Balancing Model
+5 XP
The most powerful way to think about equations is to imagine a set of balance scales. When an equation is true, the scales are perfectly level.
The equals sign is the pivot of the scales. The LHS sits in the left pan; the RHS sits in the right pan. If both pans hold the same total weight, the scales are level — the equation is true. The golden rule: whatever you do to one side, do the same to the other side.
$\text{LHS} = \text{RHS}$
Scales are level
An equation tells us the two sides are already balanced. The equals sign is the pivot.
Do the same to both sides
Add 3 to the left? Add 3 to the right. Multiply the left by 2? Multiply the right by 2. Always.
Why it works
Treating both sides the same keeps the balance. Changing only one side tips the scales — the equation becomes false.
5
Checking by Substitution
+5 XP
To check whether a value is the solution, substitute it into the equation and compare both sides.
Is $x = 3$ a solution of $2x + 1 = 7$?
Substitute: LHS $= 2(3) + 1 = 7$. RHS $= 7$. LHS $=$ RHS ✓ Yes, $x = 3$ is the solution.
Is $x = 5$ a solution of $3x - 4 = 10$?
Substitute: LHS $= 3(5) - 4 = 11$. RHS $= 10$. LHS $\neq$ RHS ✗ No, $x = 5$ is not the solution.
Try It Now: Is $x = 4$ a solution of $x + 8 = 12$? Substitute and compare.
Answer: LHS = $4 + 8 = 12$ = RHS ✓ Yes!
Watch Me Solve It · Worked example
Watch Me Solve It · Check a solution
+15 XP per step
Q
PROBLEM
Check whether $x = 4$ is a solution of $5x - 3 = 17$.
1
Substitute $x = 4$ into the LHS
$5(4) - 3 = 20 - 3 = 17$
Replace every $x$ with the value 4. Then evaluate the expression step by step using order of operations — multiplication before subtraction.
2
Compare LHS with RHS
LHS $= 17$ and RHS $= 17$
The RHS of the equation is 17. Our LHS calculation also gave 17, so both sides are equal.
3
Write the conclusion
LHS $=$ RHS ✓ Therefore $x = 4$ is the solution.
Since substituting $x = 4$ makes both sides equal, the equation is balanced. $x = 4$ is confirmed as the solution.
Nice work — XP earned
AnswerYes, $x = 4$ is the solution because $5(4) - 3 = 17 = $ RHS.
6
Common Pitfalls
heads-up
Thinking = means "the answer"
Many students read $2x + 1 = 7$ and think "equals just means the result." In algebra, = means balance — the left side and right side have the same value.
Fix: picture the balance scales every time you see an equals sign. Both sides must weigh the same.
Only substituting into one side
Substituting into the LHS and getting a number, then stopping — without checking if that number equals the RHS — is incomplete work.
Fix: always compare both sides. Write "LHS = ___ , RHS = ___" and check they match before concluding.
Confusing expression with equation
Trying to "solve" $3x + 5$ has no meaning — there is nothing to solve without an equals sign. Only equations have solutions.
Fix: scan for the = sign first. No equals → expression (describe it, don't solve it). Has equals → equation (find the solution).
Quick Check · 5 questions
1
Which of the following is an equation?
+10 XP
2
Is $x = 5$ a solution to $3x + 2 = 17$?
+10 XP
3
What are the LHS and RHS of $4x - 3 = 9$?
+10 XP
4
"Three times a number, decreased by 4, equals 11." Which equation matches?
+10 XP
5
Is $x = 2$ a solution to $x^2 + 3 = 7$?
+10 XP
ApplyEasy2 MARKS
Q1. State whether each is an expression or an equation: (a) $5x - 3 = 12$ (b) $2a + 7b$ (c) $y^2 = 16$
Answer in your workbook.
ApplyMedium3 MARKS
Q2. Check whether $x = 6$ is a solution to $2x - 5 = 7$. Show your working.
Answer in your workbook.
ApplyHard4 MARKS
Q3. Write an equation for: "Five more than twice a number is equal to twenty-one." Then identify the LHS and RHS.
Answer in your workbook.
Stretch Challenge · +25 XP, +10 coins
Extension Problems
Write an equation for: "The sum of three consecutive numbers is 48." Define your variable carefully!...
R
Quick Review
Key Concept
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Formulas
Key formulas and rules.
Watch Out
Common mistakes to avoid.
Check
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Practice
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Next
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Interactive: Algebra Machine
Substitute numbers into algebraic expressions and see them evaluate step by step.
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