Solving Linear Equations — SAT Math Explained
A linear equation is an equation where the variable appears to the first power only, producing a straight-line graph. Solving it means finding the specific value of the variable that makes the equation true.
The Core Idea
Whatever operation is applied to one side of the equation must be applied to the other side to keep balance. You work backwards through the order of operations to peel away everything around the variable.
Key Vocabulary
A letter standing in for an unknown number (e.g., x, y, n)
The number multiplied by a variable (in 3x, the coefficient is 3)
A fixed number with no variable attached
The value of the variable that satisfies the equation
The operation that undoes another — subtraction undoes addition, division undoes multiplication
Step-by-Step: How to Approach Solving Linear Equations
Simplify both sides by combining like terms and distributing
Move all variable terms to one side using addition/subtraction
Move all constants to the other side
Divide both sides by the coefficient of the variable
Check your answer by substituting back into the original equation
Types Of Solutions
The variable equals exactly one number (e.g., x = 5) — this is the standard case
The variable cancels out and you're left with a false statement like 3 = 7, meaning no value works
The variable cancels and you get a true statement like 0 = 0, meaning every number works
Visual Representation
On a number line, the solution is a single point. On a coordinate plane, a linear equation graphs as a perfectly straight line.
Common Errors to Avoid
Forgetting to distribute a negative sign across parentheses
Adding when you should subtract to move terms
Not checking the solution in the original equation
How This Connects to Other Topics
Forms the foundation for multi-step equations, systems of equations, and all function-based work
Practice: Solving Linear Equations
5 SAT-style questions. Select your answer and get an instant explanation.
Solve for x: 3x + 7 = 22
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