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Chapter 2: Problem 27

Solve each equation, and check your solution. $$ t+12.3=-4.6 $$

Short Answer

Expert verified
The solution is t = -16.9.

Step by step solution

01

- Isolate the Variable

Start by isolating the variable on one side of the equation. We have the equation:t + 12.3 = -4.6To isolate t, subtract 12.3 from both sides of the equation.
02

- Perform the Subtraction

Subtract 12.3 from both sides of the equation:t + 12.3 - 12.3 = -4.6 - 12.3This simplifies to:t = -16.9
03

- Check Your Solution

To verify the solution, substitute t = -16.9 back into the original equation:t + 12.3 = -4.6Substitute t with -16.9:-16.9 + 12.3 = -4.6Simplify the left side:-4.6 = -4.6Since both sides of the equation are equal, the solution t = -16.9 is correct.

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Key Concepts

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

Isolating the Variable
Isolating the variable means getting the variable by itself on one side of the equation. In our exercise, the initial equation is:
\( t + 12.3 = -4.6 \).
To isolate \( t \), we want to remove the constant term (12.3) from the left side. We do this by performing the same operation on both sides of the equation. In this case, we subtract 12.3 from both sides:
\( t + 12.3 - 12.3 = -4.6 - 12.3 \).
By doing so, we simplify the equation to:
\( t = -16.9 \).
This gives us our isolated variable.
Performing Arithmetic Operations
Performing arithmetic operations correctly is crucial in solving equations. In this exercise, we subtracted 12.3 from both sides of the equation to isolate \( t \). It's important to always perform the same operation on both sides to maintain balance in the equation.

Let's break down the arithmetic we did:
On the left side: \( t + 12.3 - 12.3 \) simplifies to \( t \) because adding and then subtracting the same number cancels it out.
On the right side: \( -4.6 - 12.3 \) results in \( -16.9 \).
Doing these operations step-by-step ensures we get the correct value for \( t \).
Checking Solutions
After solving for the variable, it's essential to check your solution by substituting it back into the original equation. This ensures that our solution is correct.

In this case, we found \( t = -16.9 \).
We substitute \( t \) back into the original equation:
\( t + 12.3 = -4.6 \)
Substitute \( t \) with \( -16.9 \): \( -16.9 + 12.3 = -4.6 \)
Simplify the left side: \( -4.6 = -4.6 \).
Since both sides of the equation are equal, this verifies that the solution \( t = -16.9 \) is correct.

Remember to always check your solutions to confirm accuracy.

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