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MathematicsGrade 8· U.S. National — Common Core & NGSS
Aligned to:Common Core State Standards (Math)

Solving Linear Equations

Isolate the variable, balance both sides, and check your answer on one- and two-step equations.

Solving Linear Equations

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What an equation asks

A linear equation says two expressions are equal. Solving it means finding the value of the variable that keeps the statement true. Think of the equal sign as a balance point: whatever you do to one side, you must do to the other.

One- and two-step solutions

Undo operations in reverse order. For 3x + 5 = 20, subtract 5 from both sides to get 3x = 15, then divide both sides by 3 to get x = 5. Addition undoes subtraction and division undoes multiplication.

Variables on both sides, and checking

When the variable appears on both sides, collect like terms first: 5x - 4 = 2x + 11 becomes 3x = 15, so x = 5. Always substitute your answer back into the original equation to confirm both sides match.