Patterns and Algebra - Solving One-Step Equations

An algebraic equation is a mathematical statement showing that two expressions are equal, represented by the equals sign ($=$). Think of it like a balanced scale where both sides must have the same total value to remain level.

A variable is a letter, such as $x$ or $n$, that represents an unknown number we are trying to find. The goal of solving a one-step equation is to isolate the variable on one side of the equals sign.

Inverse operations are 'opposite' operations that undo each other. Addition ($+$) and subtraction ($-$) are inverse operations, while multiplication ($\times$) and division ($\div$) are inverse operations.

The Golden Rule of Algebra states that to keep an equation balanced, whatever operation you perform on one side of the equals sign, you must perform the exact same operation on the other side. If you visualize a balance scale, adding $5$kg to one side requires adding $5$kg to the other to maintain equilibrium.

To solve an addition equation like $x + 5 = 12$, you use the inverse operation of subtraction. You subtract $5$ from both sides to find that $x = 7$.

To solve a subtraction equation like $x - 8 = 10$, you use the inverse operation of addition. You add $8$ to both sides to find that $x = 18$.

To solve a multiplication equation like $3x = 15$, you use the inverse operation of division. By dividing both sides by $3$, you isolate the variable to find $x = 5$.

To solve a division equation like $\frac{x}{4} = 6$, you use the inverse operation of multiplication. Multiplying both sides by $4$ cancels out the division and reveals that $x = 24$.