91Ó°ÊÓ

Algebra involves working with variables, numbers, and operations to solve equations and understand relationships within mathematics. In this exercise, we are given an equation involving a variable. The variable is represented by the letter \( t \) and is shown in the context of a multiplication equation: \( 56 = 7t \). Here, algebra helps us manipulate the equation to solve for the unknown variable. The goal is to isolate \( t \), meaning we want to get \( t \) alone on one side of the equation. Understanding these basic operations and definitions is key to solving algebraic equations.

Solving equations is a fundamental aspect of algebra. It involves finding the value of a variable that makes the equation true. In our specific problem, the first step is to identify the given equation: \( 56 = 7t \).
To solve for \( t \), we use the multiplication principle. This principle allows us to 'undo' the multiplication of \( t \) by 7. We divide both sides of the equation by 7 to isolate \( t \). This action is represented as: \( \frac{56}{7} = \frac{7t}{7} \).
Simplifying these fractions gives: \( 8 = t \). This means the value of \( t \) that makes the initial equation true is 8. It is important to perform the same mathematical operation on both sides of the equation to maintain equality.

Verification of solutions is an essential step in solving equations. After finding the value of a variable, you should always check your solution by substituting the variable back into the original equation. This ensures the solution is correct. For our equation \( 56 = 7t \), we found that \( t \) is equal to 8.
To verify, we substitute \( t = 8 \) back into the original equation: \( 56 = 7 \times 8 \). Simplifying the right side, we get \( 56 = 56 \). Since both sides of the equation are equal, our solution is verified to be correct. Verification prevents errors and confirms that the solution is valid and accurate.