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Chapter 5: Problem 39

Solve. $$ t+4.25=8.7 $$

Short Answer

Expert verified
t = 4.45

Step by step solution

01

Write Down the Equation

Start by writing down the given equation: t + 4.25 = 8.7
02

Isolate the Variable

To solve for the variable t, isolate it by subtracting 4.25 from both sides of the equation: t + 4.25 - 4.25 = 8.7 - 4.25This simplifies to: t = 4.45
03

Verify the Solution

Finally, verify the solution by substituting t back into the original equation to ensure both sides are equal. t + 4.25 = 8.74.45 + 4.25 = 8.78.7 = 8.7Since both sides are equal, the solution is correct.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Basic Algebra
Basic algebra involves working with variables and constants to find unknown values. In our exercise, the equation given was: \(t + 4.25 = 8.7\). Here, \(t\) is the variable, and 4.25 and 8.7 are constants. The goal is to solve for \(t\), meaning we need to find what value of \(t\) makes the equation true. Understanding how to manipulate equations by performing the same operation on both sides is crucial for maintaining equality. Basic algebra lays the foundation for more advanced mathematics and is useful in various real-life situations, such as budgeting or calculating distances.
Isolating Variables
Isolating the variable is a critical step when solving linear equations. To isolate \(t\) in the equation \(t + 4.25 = 8.7\), we need to undo the addition of 4.25 to \(t\). This is done by subtracting 4.25 from both sides of the equation, which keeps the balance. Here鈥檚 how:
  • Start with the equation: \(t + 4.25 = 8.7\).
  • Subtract 4.25 from both sides: \(t + 4.25 - 4.25 = 8.7 - 4.25\).
This simplifies to \(t = 4.45\).By isolating the variable, we can determine its value, making it straightforward to solve the equation.
Verifying Solutions
Verifying solutions ensures that the value found for the variable is indeed correct. After solving for \(t\), we found that \(t = 4.45\). To verify, substitute \(t\) back into the original equation.
  • Original equation: \(t + 4.25 = 8.7\).
  • Substitute \(t\) with 4.45: \(4.45 + 4.25 = 8.7\).
  • Calculate the left side: 4.45 + 4.25 equals 8.7.
Since both sides of the equation are equal, our solution \(t = 4.45\) is verified as correct. Verifying is important as it confirms the accuracy of our solution and catches any potential mistakes made during the solving process.

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