This understanding involves maintaining equality while simplifying expressions with the distributive property, combining like terms, and applying inverse operations to solve linear equations in one variable with integer, decimal, and fractional coefficients, including variables on both sides. It includes interpreting one solution, no solution, or infinitely many solutions and recognizing that each transformation must preserve the equation’s solution set; the scope excludes nonlinear equations, systems, and more abstract parameterized cases, while supporting later work with functions, graphs, and algebraic modeling.
To solve a multi-step linear equation, simplify both sides while keeping the equation balanced. Whatever operation you perform on one side, perform on the other side as well.
Example:
1. Use the distributive property.
Multiply by each term inside the parentheses:
2. Combine like terms.
On the left, combine and :
3. Move the variable terms to one side.
Subtract from both sides:
Simplify:
4. Move the constant term.
Add to both sides:
5. Isolate the variable.
Divide both sides by :
6. Check the solution.
Substitute for in the original equation:
Because the statement is true, the solution is
Each step preserves the equation’s equality, so it preserves the solution.
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