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When we talk about solving equations in algebra, it involves finding the value of unknown variables that satisfy the equation. An equation is a mathematical statement that asserts the equality of two expressions.
In the given exercise, the equation is derived from the formula for simple interest: \[I = prt\]Here, \(I\) is the interest, \(p\) is the principal amount, \(r\) is the rate of interest, and \(t\) is the time period. Our task is to solve for \(t\), making it the subject of the equation.An effective way to solve an equation is to use operations that will allow the variable to stand alone on one side of the equation. This process leads to a clearer understanding and prepares us to substitute values into the equation, which is critical in finding specific results from algebraic expressions.

Interest calculation is a crucial concept in both mathematics and finance, primarily concerned with determining how much interest an investment will earn or loan will cost over time. Simple interest is a straightforward way of calculating this, where the interest amount does not compound.In the formula \[I = prt\]where:

• \(I\) is the interest accrued or paid.
• \(p\) is the initial principal balance.
• \(r\) is the rate of interest, expressed as a decimal.
• \(t\) is the time period that the money is invested or borrowed for.

The given exercise requires substituting in known values to determine the time taken to accumulate a specific interest amount. By learning how to handle these calculations, students can predict future interest payments or gains, making this an essential skill for financial literacy.

Isolation of variables is a technique used in algebra to solve for a specific variable within an equation. This involves performing operations that shift other components of the equation away from the variable of interest.Consider the equation from the exercise: \[I = prt\]To solve for \(t\), our goal was to manipulate the equation such that \(t\) is alone on one side. We achieve this by dividing both sides by \(pr\), resulting in:\[t = \frac{I}{pr}\]This "isolation" has produced a direct formula where \(t\) can be easily calculated if \(I\), \(p\), and \(r\) are known.Understanding how to isolate variables is at the core of algebraic problem-solving. It transforms complex equations into simpler forms, making them more manageable and allowing for easier computation and interpretation.