A solution to a linear equation is a value for the variable that makes both sides equal; interpreting it means relating that value to the quantities and conditions represented by the equation and verifying it in the original equality. Symbolic, tabular, and coordinate representations show that a one-variable linear equation typically identifies one value, while simplification may reveal no solution or infinitely many solutions through a contradiction or identity. Systems and more advanced parameterized cases are outside this scope.
A solution to a linear equation is a value of the variable that makes the left side and right side equal. To interpret a solution, explain what the value means in the situation and check it in the original equation.
Example: A taxi charges a 5$3$20$. How many miles were traveled?
Let represent the number of miles. The equation is
Subtract from both sides:
Divide both sides by :
The solution means the taxi traveled 5 miles.
Substitute into the original equation:
Both sides are equal, so is the solution. It also makes sense in the situation because a distance of miles is valid.
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