Solving Linear Equations in One Variable

Solving Linear Equations in One Variable

A linear equation in one variable is an equation that can be written in the form:

$$ax + b = c$$

where $a$, $b$, and $c$ are real numbers and $a \neq 0$.

Golden Rule of Equations

Whatever mathematical operation you perform on one side of an equation, you must perform on the other side.

Step-by-Step Method:

1. Simplify each side: Distribute parentheses and combine like terms.
2. Isolate variable terms: Use addition or subtraction to get all variable terms on one side and constants on the other.
3. Isolate the variable: Use multiplication or division to make the variable's coefficient equal to $1$.
4. Check your answer: Substitute your solution back into the original equation.

Worked Example:

Solve for $x$: $$3(x - 4) + 2 = 14$$

Step 1: Distribute the $3$: $$3x - 12 + 2 = 14$$ $$3x - 10 = 14$$