Let's break down the problem step by step.
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Write the equation: The statement "A number decreased by sixty-eight is thirty-one" can be translated into the equation: \[ x - 68 = 31 \] where \( x \) is the number we're trying to find.
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Solve the equation: To solve for \( x \), we need to isolate \( x \) on one side. We do this by adding 68 to both sides of the equation: \[ x - 68 + 68 = 31 + 68 \] Simplifying this gives: \[ x = 99 \]
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Check the solution: Now we check the solution by substituting \( 99 \) back into the original equation: \[ 99 - 68 = 31 \] Simplifying the left side: \[ 31 = 31 \] This statement is true, so our solution is verified.
Now, we can fill in the blanks based on the above steps:
- Equation: \( x - 68 = 31 \)
- To solve the equation, add 68 to both sides of the equation.
- To check the solution, substitute 99 for the variable in the equation.
These statements accurately convey the steps taken to solve the problem.