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Chapter 5: Problem 13

Solve the equations. $$t-3.92=-8.7$$

Short Answer

Expert verified
t = -4.78

Step by step solution

01

Isolate the Variable

Start by isolating the variable on one side of the equation. To do this, add 3.92 to both sides to cancel out the -3.92 on the left.
02

Add 3.92 to Both Sides

Calculate the left side: \( t - 3.92 + 3.92 = -8.7 + 3.92 \)
03

Simplify the Equation

Simplify both sides to find:\( t = -4.78 \)

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Key Concepts

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

isolating the variable
The first step in solving the equation is to isolate the variable. In our example, the equation is: \( t - 3.92 = -8.7 \).
To isolate the variable (\( t \)), you need to get \( t \) by itself on one side of the equation.
This will make it easier to solve for \( t \) because you will have a simple equation where \( t \) equals a constant. To achieve this, you need to eliminate the other numbers from the side of the equation that \( t \) is on.
In this case, that number is \(-3.92\). By performing the same operation on both sides of the equation, you maintain the balance of the equation, which is crucial.
addition in equations
Next, we need to use addition to get rid of the \(-3.92\) next to \( t \).
By adding \( 3.92 \) to both sides of the equation:
\( t - 3.92 + 3.92 = -8.7 + 3.92 \),
The \( -3.92 \) and \( +3.92 \) will cancel each other out on the left side, resulting in just \( t \) on that side.
This leaves you with a new, simplified equation: \( t = -4.78 \).
This step is crucial because adding or subtracting the same number on both sides of the equation keeps it balanced, which allows you to solve for the variable accurately.
simplifying equations
In the final step, we simplified the equation to find the value of \( t \).
After adding \( 3.92 \) to both sides, we obtained: \( t = -4.78 \).
The equation is now simplified, with \( t \) isolated and equal to \(-4.78\).
Simplifying equations involves combining like terms and performing arithmetic operations.
This ensures the variable is isolated and the equation is straightforward to interpret.
Simplification makes complex equations much more manageable and helps verify the solution by substituting the variable back into the original equation to check its correctness.

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