Algebra / Linear Equations One Variable
Linear Equations in One Variable
Linear equations in one variable ask for the value of a single unknown that makes an equation true. Common moves include distributing, combining like terms, clearing fractions, and using inverse operations.
Least you need to know
- A linear equation in one variable can often be solved by isolating the variable.
- Equivalent operations may be applied to both sides of an equation.
- Some linear equations have one solution, no solution, or infinitely many solutions.
Key notation
- x — The unknown value in a one-variable equation
Worked example
- Consider $3(x-2)+5=20$.
- Distribute: $3x-6+5=20$.
- Combine like terms: $3x-1=20$.
- Add 1 to both sides: $3x=21$.
- Divide by 3: $x=7$.
Common mistakes
- Distribute to every term inside parentheses.
- When clearing fractions, multiply every term on both sides.
- A variable that cancels out may indicate no solution or infinitely many solutions.
How to recognize it
- The problem asks for the value of one variable.
- The equation can be simplified to a form such as $ax+b=c$ or $ax+b=cx+d$.
- The problem may ask for a transformed quantity such as $x+3$ instead of $x$.
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