This understanding involves transforming one-variable linear equations, including those with parentheses, like terms, rational coefficients, and variables on both sides, through equivalent operations that preserve the equality. It includes interpreting the resulting solution, recognizing when an equation has one solution, no solution, or infinitely many solutions, and checking by substitution rather than treating every equation as having a single answer. The scope excludes systems of equations, nonlinear equations, and more advanced parameterized or abstract cases.
To solve a multi-step linear equation, simplify both sides using operations that keep the equation balanced. Whatever you do to one side, do to the other side.
Example:
1. Distribute across the parentheses:
2. Combine like terms on the left:
3. Move variable terms to one side. Subtract from both sides:
4. Move constant terms to the other side. Subtract from both sides:
5. Divide by the coefficient of :
So, the solution is .
Check the solution by substituting into the original equation:
Since both sides equal , is correct.
Sometimes, simplifying an equation makes the variable cancel. If a true statement remains, such as , there are infinitely many solutions. If a false statement remains, such as , there is no solution.
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