What Is a Simple Equation?

An equation is a mathematical statement that shows that two expressions are equal (they have an “ = ” sign).

A simple equation is one where the unknown (or variable) appears only once or in a straightforward way, and can be solved using basic operations.

Examples:

3x + 5 = 20
5n − 4 = 11
2y = 14
½x + 3 = 7

These are “simple” because we don’t have too many variables, powers, or complicated forms.

1. Because many real-life problems lead to equations.


2. To find unknown values in problems (ages, money, length, etc.).


3. To prepare for more advanced algebra (linear equations, systems, quadratics).


4. Because the JSS2 curriculum includes “Simple Equations” as a key topic.

1. Understand what an equation is (two expressions equal).


2. Identify unknowns and write equations from statements.


3. Solve simple linear equations using basic operations (addition, subtraction, multiplication, division).


4. Use balancing methods (doing the same operation to both sides).


5. Check their solutions by substituting back into original equation.


6. Solve word problems that lead to simple equations.

1. The “Balance” Idea

An equation can be thought of like a balance scale: whatever you do to one side, you must do to the other so the equality remains true.

2. Isolating the Unknown (x or n or y)

You try to get the unknown by itself (on one side) by undoing whatever is done to it.

1. If the unknown has something added or subtracted, do the inverse operation (subtract or add) to both sides.


2. If the unknown is multiplied, divide both sides.


3. If the unknown is divided, multiply both sides.

3. Combining Like Terms

Before isolating, combine similar terms if needed (e.g. 3x + 2x = 5x).

4. Checking the Solution

After finding a value, substitute back into the original equation to see if both sides equal.

5. Equations with Fractions or Brackets

Sometimes equations will include brackets or fractions. You first expand brackets or clear fractions before the basic operations.

1. Rewrite / simplify both sides (remove brackets, combine like terms).


2. Move terms involving the unknown to one side, constants to the other side (using addition/subtraction).


3. Divide or multiply to isolate the unknown.


4. Verify / check your result in the original equation.


5. State your final answer clearly.

1. Doing something to only one side (breaking balance).


2. Forgetting to change signs when moving terms across the “ = ”.


3. Dividing before subtracting (wrong order of operations).


4. Forgetting to check the answer in the original equation.


5. Making arithmetic errors with negatives.


6. Misreading bracketed expressions or not expanding them first.

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Simple Equations examples

1. Solve for x:

3x + 4 = 13

Step 1: Subtract 4 from both sides.
3x = 13 − 4
3x = 9

Step 2: Divide both sides by 3.
x = 9 ÷ 3
x = 3

Answer: x = 3

2. Solve for y:

7y − 5 = 23

Step 1: Add 5 to both sides.
7y = 23 + 5
7y = 28

Step 2: Divide both sides by 7.
y = 28 ÷ 7
y = 4

Answer: y = 4

3. Solve for n:

4n = 28

Step 1: Divide both sides by 4.
n = 28 ÷ 4
n = 7

Answer: n = 7

4. Solve for p:

6p ÷ 2 = 15

Step 1: Simplify the left side.
(6 ÷ 2)p = 15
3p = 15

Step 2: Divide both sides by 3.
p = 15 ÷ 3
p = 5

Answer: p = 5

5. Solve for a:

a/3 + 5 = 11

Step 1: Subtract 5 from both sides.
a/3 = 11 − 5
a/3 = 6

Step 2: Multiply both sides by 3.
a = 6 × 3
a = 18

Answer: a = 18

6. Solve for x:

5x − 3 = 2x + 9

Step 1: Move all x terms to one side and constants to the other.
5x − 2x = 9 + 3
3x = 12

Step 2: Divide both sides by 3.
x = 12 ÷ 3
x = 4

Answer: x = 4

7. Solve for m:

4m + 8 = 2m + 20

Step 1: Move 2m to the left and 8 to the right.
4m − 2m = 20 − 8
2m = 12

Step 2: Divide both sides by 2.
m = 12 ÷ 2
m = 6

Answer: m = 6

8. Solve for k:

10 − 2k = 4k − 2

Step 1: Add 2k to both sides.
10 = 6k − 2

Step 2: Add 2 to both sides.
12 = 6k

Step 3: Divide both sides by 6.
k = 12 ÷ 6
k = 2

Answer: k = 2

9. Solve for x:

(x/2) + 3 = 7

Step 1: Subtract 3 from both sides.
x/2 = 7 − 3
x/2 = 4

Step 2: Multiply both sides by 2.
x = 4 × 2
x = 8

Answer: x = 8

10. Solve for y:

2(y − 4) = 10

Step 1: Expand the bracket.
2y − 8 = 10

Step 2: Add 8 to both sides.
2y = 18

Step 3: Divide both sides by 2.
y = 18 ÷ 2
y = 9

Answer: y = 9

Bonus Challenge:

3x + 7 = 2x + 12

Step 1: Subtract 2x from both sides.
x + 7 = 12

Step 2: Subtract 7 from both sides.
x = 12 − 7
x = 5

Answer: x = 5