Final answer:
The equation 834 = 17 - x means '834 is the same as 17 decreased by a number.' This concept emphasizes the importance of viewing equations as expressions of relationships and ideas rather than just number-crunching tools.
Step-by-step explanation:
The equation 834 = 17 - x represents a mathematical sentence that establishes a relationship between different numbers and variables. In this case, the number 834 is equal to the difference obtained when a number x is subtracted from 17. The correct representation of this equation, in sentence form, is option c: 834 is the same as 17 decreased by a number.
When looking at equations, it's important to recognize that they are not just machines for plugging in numbers; they convey precise relationships and concepts. Understanding these relationships helps us make sense of and solve these mathematical statements. For instance, when we invert a term, like dividing by x, we are essentially looking at the negative power of that number, which means putting the variable in the denominator - as shown by the expression x-1 = 1/x.
Additionally, we often deal with quadratic equations, generally of the form at2 + bt + c = 0. These equations are solved using the quadratic formula. Whether the equation looks complicated or you're looking to solve for a single variable, the process holds consistent through the application of mathematical rules and operations.