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Interpret solutions to linear equations

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.

Detailed Explanation: Interpret solutions to linear equations

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 5startingfeeplusstarting fee plus$3permile.Thetotalcostisper mile. The total cost is$20$. How many miles were traveled?

Let mm represent the number of miles. The equation is

3m+5=203m+5=20

Step 1: Solve the equation

Subtract 55 from both sides:

3m=153m=15

Divide both sides by 33:

m=5m=5

Step 2: Interpret the solution

The solution (m=5)(m=5) means the taxi traveled 5 miles.

Step 3: Verify the solution

Substitute 55 into the original equation:

3(5)+5=203(5)+5=20 15+5=2015+5=20 20=2020=20

Both sides are equal, so (m=5)(m=5) is the solution. It also makes sense in the situation because a distance of 55 miles is valid.

Learn by doing: Interpret solutions to linear equations

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Verify a Solution to a Linear Equation - Single Equation to True or False


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