Addition Equation

Solve: $x + 7 = 15$

Identify what's happening to $x$: $x$ has $7$ added to it = Operation: addition

Use the inverse operation: The inverse of addition is subtraction = Subtract $7$ from both sides

Subtract $7$ from both sides: $x + 7 - 7 = 15 - 7$ = $x = 8$

Check your answer: $8 + 7 = 15$ ✓ = Correct!

Answer: $x = 8$

Subtraction Equation

Solve: $y - 9 = 14$

Identify what's happening to $y$: $y$ has $9$ subtracted from it = Operation: subtraction

Use the inverse operation: The inverse of subtraction is addition = Add $9$ to both sides

Add $9$ to both sides: $y - 9 + 9 = 14 + 9$ = $y = 23$

Check your answer: $23 - 9 = 14$ ✓ = Correct!

Answer: $y = 23$

Multiplication Equation

Solve: $5n = 35$

Identify what's happening to $n$: $n$ is multiplied by $5$ = Operation: multiplication

Use the inverse operation: The inverse of multiplication is division = Divide both sides by $5$

Divide both sides by $5$: $\frac{5n}{5} = \frac{35}{5}$ = $n = 7$

Check your answer: $5 \times 7 = 35$ ✓ = Correct!

Answer: $n = 7$

Division Equation

Solve: $\frac{m}{4} = 6$

Identify what's happening to $m$: $m$ is divided by $4$ = Operation: division

Use the inverse operation: The inverse of division is multiplication = Multiply both sides by $4$

Multiply both sides by $4$: $\frac{m}{4} \times 4 = 6 \times 4$ = $m = 24$

Check your answer: $\frac{24}{4} = 6$ ✓ = Correct!

Answer: $m = 24$

Word Problem

Maria has some stickers. After giving 12 stickers to her friend, she has 28 left. How many stickers did she start with?

Define the variable: Let $s$ = stickers Maria started with = $s$ is the unknown

Write the equation: Started with $s$, gave away $12$, left with $28$ = $s - 12 = 28$

Solve using inverse operation: $s - 12 + 12 = 28 + 12$ = $s = 40$

Check and interpret: $40 - 12 = 28$ ✓ = Maria started with 40 stickers

Answer: Maria started with $40$ stickers

Mistake: Using the same operation instead of the inverse

Why: Students sometimes add when they should subtract, or multiply when they should divide.

Correct: Remember: to undo addition, subtract. To undo subtraction, add. To undo multiplication, divide. To undo division, multiply.

Mistake: Only applying the operation to one side

Why: The equation becomes unbalanced and the solution is wrong.

Correct: Always do the same thing to BOTH sides of the equation. Think of a balance scale!

Mistake: Forgetting to check the answer

Why: Without checking, you might not catch arithmetic errors.

Correct: Always substitute your answer back into the original equation to verify.

Mistake: Confusing $3x$ with $x + 3$

Why: $3x$ means $3 \times x$ (multiplication), while $x + 3$ is addition.

Correct: $3x = 15$ needs division: $x = 5$. But $x + 3 = 15$ needs subtraction: $x = 12$.

Shopping Budget

Calculating how much you can spend or need to save.

You want to buy a book that costs 18 euros. You have 11 euros. How much more do you need? Equation: $11 + x = 18$, so $x = 7$ euros.

Recipe Scaling

Adjusting recipes for different numbers of servings.

A recipe makes 6 cookies per batch. You need 42 cookies for a party. How many batches? Equation: $6b = 42$, so $b = 7$ batches.

Sports Statistics

Finding unknown scores or statistics in games.

A basketball player scored 23 points total. She made 8 points from free throws. How many points were from field goals? Equation: $x + 8 = 23$, so $x = 15$ points.

Q: How do I know which operation to use?

A: Look at what's being done to the variable and do the opposite. If the variable has something added to it, subtract. If multiplied, divide. And vice versa.

Q: Why do I have to do the same thing to both sides?

A: An equation is like a balance scale. If you add weight to one side, you must add the same weight to the other side to keep it balanced. The same applies to equations.

Q: What if the variable is on the right side?

A: The process is the same! For example, in $15 = x + 7$, subtract $7$ from both sides to get $8 = x$, which is the same as $x = 8$.