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When solving linear equations, one of the primary goals is to isolate the variable. This means you want to get the variable by itself on one side of the equation. In the equation \(8.9 = -4.1 + t\), your variable is \(t\).
To isolate \(t\), perform the opposite operation of what's being done to it. Since \(-4.1\) is being added to \(t\), you should add \(4.1\) to both sides of the equation. This cancels out the \(-4.1\) on the right side.
By doing this, you manipulate the equation to say:

• \(8.9 + 4.1 = t\)

This step is crucial as it transforms a more complex equation into a simple arithmetic problem, making it easier to solve for \(t\). Being methodical and consistent with isolating the variable helps prevent errors and makes complex problems more manageable.

Verification is a critical step in solving equations to ensure the solution is correct. After isolating the variable, substitute the found value back into the original equation to verify correctness. For example, we've found that \(t = 13.0\).
When you substitute \(t = 13.0\) back into \(8.9 = -4.1 + t\), it should make both sides of the equation equal:

• \(8.9 = -4.1 + 13.0\)
• Calculate: \(-4.1 + 13.0 = 8.9\)

If both sides come out equal, it confirms the solution is correct. Checking solutions helps to eliminate possible errors that might have occurred during initial calculations.
Creating this habit reinforces accuracy and confidence in your math skills.

Arithmetic operations such as addition, subtraction, multiplication, and division, are foundational when solving equations. These operations let you manipulate equations to isolate variables effectively.
In the equation \(8.9 = -4.1 + t\), use addition to solve it. By recognizing that \(-4.1\) is on the same side as \(t\), adding \(4.1\) helps you cancel out the negative term. This aligns with one of the fundamental properties of equality: doing the same operation on both sides of an equation keeps it balanced.
Here's the arithmetic step played out:

• Add \(4.1\) to both sides: \(8.9 + 4.1 = t\)
• Simplify: \(13.0 = t\)

Mastering these arithmetic steps is essential for solving equations quickly and efficiently. Understanding how and why you perform each operation builds a strong foundation for more advanced math concepts.