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The distributive property is a fundamental concept in algebra that helps in simplifying expressions. It allows us to "distribute" or multiply a single term across terms inside a parenthesis. In the given equation, we apply the distributive property to the expression \(0.3(2t + 0.1)\). This means we multiply 0.3 by each term inside the parentheses:

• 0.3 is multiplied by \(2t\), which results in \(0.6t\).
• 0.3 is also multiplied by 0.1, resulting in 0.03.

After applying the distributive property, our equation becomes \(0.6t + 0.03 = 8.43\).
Practicing the distributive property helps in breaking down more complex equations and makes it easier to manage multiple terms. It is particularly useful when equations involve parentheses, leading to simpler and often more straightforward expressions.

Isolating the variable means arranging the equation so that the variable is on one side of the equation by itself. This helps in clearly seeing the value that the variable represents. In the expression \(0.6t + 0.03 = 8.43\), our goal is to have \(t\) by itself on one side.
The first step is to remove any constants from the side with the variable. We do this by subtracting 0.03 from both sides of the equation:

• On the left side: \(0.6t + 0.03 - 0.03 = 0.6t\).
• On the right side: \(8.43 - 0.03 = 8.4\).

Now, our equation simplifies to \(0.6t = 8.4\).
Isolating the variable ensures you're working with a more straightforward equation that is easier to solve. This step is crucial in making final calculations to find the value of unknowns in equations.

Solving a linear equation involves finding the value of the variable that makes the equation true. After isolating the variable, the next step is to solve for it explicitly. The current equation is \(0.6t = 8.4\).
To solve for \(t\), divide both sides by 0.6:

• The left side becomes: \(\frac{0.6t}{0.6} = t\).
• The right side becomes: \(\frac{8.4}{0.6} = 14\).

Thus, \(t = 14\) is the solution to the equation.
Solving linear equations typically involves operations such as addition, subtraction, multiplication, and division. These operations simplify the equation, allowing you to find the precise value of the variable. Mastering this skill aids in tackling more complex algebraic problems efficiently.