When solving an equation, we find the value of the variable that makes the equation true. The key rule is: whatever we do to one side, we must do to the other side.

Solving by Addition

When the variable has a number added to it, subtract that number from both sides.

Example: Find the value of $p$ in $p + 2 = 8$

Solution: $p + 2 - 2 = 8 - 2$ $p = 6$

Solving by Subtraction

When the variable has a number subtracted from it, add that number to both sides.

Example: Find the value of $k$ in $k - 5 = 12$

Solution: $k - 5 + 5 = 12 + 5$ $k = 17$

Solving by Multiplication

When the variable is multiplied by a number, divide both sides by that number.

Example: Find the value of $n$ in $4n = 36$

Solution: $\frac{4n}{4} = \frac{36}{4}$ $n = 9$

Solving by Division

When the variable is divided by a number, multiply both sides by that number.

Example: Find the value of $x$ in $x \div 3 = 7$

Solution: $\frac{x}{3} = 7$ $x = 7 \times 3$ $x = 21$

Sometimes the variable appears on both sides of the equation. First, collect all variable terms on one side.

Example: Find the value of $x$ in $7x - 6 = x + 18$

Solution:

Step 1: Move the variable from the right side to the left $7x - x = 18 + 6$

Step 2: Simplify $6x = 24$

Step 3: Divide by 6 $\frac{6x}{6} = \frac{24}{6}$ $x = 4$

In Tanzanian daily life, simple equations help with buying and selling. For example, if Amina buys a sack of maize for 25,000 shillings and wants to sell it for a profit of 8,000 shillings, she can use the equation $x - 25000 = 8000$ to find the selling price $x$. Solving this: $x = 8000 + 25000 = 33,000$ shillings. This skill is useful in markets, shops, and small businesses across Tanzania.