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Chapter 2: Problem 22

Solve using the addition principle. Don't forget to check! $$ t+6=43 $$

Short Answer

Expert verified
\( t = 37 \)

Step by step solution

01

- Identify the equation

The equation given is: \[ t + 6 = 43 \]
02

- Isolate the variable

To solve for \( t \), subtract 6 from both sides of the equation. This helps isolate the variable: \[ t + 6 - 6 = 43 - 6 \]
03

- Simplify the equation

Simplify the equation by performing the subtraction: \[ t = 37 \]
04

- Check the solution

Substitute \( t = 37 \) back into the original equation to verify. Check if the left side equals the right side: \[ 37 + 6 = 43 \] Since 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.

solving equations
When solving equations, the goal is to find the value of the unknown variable that makes the equation true. In the given exercise, the equation is \[ t + 6 = 43 \]. To solve it, you'll follow a series of steps that involve mathematical operations to isolate the variable. This process often relies on fundamental principles such as the addition and subtraction principles. These principles allow you to add or subtract the same number from both sides of the equation, maintaining the equation's balance. When you solve equations, remember to keep the equation balanced by performing the same operation on both sides. This ensures that the equality remains valid.
isolating variables
Isolating the variable is a critical step in solving equations. To have the variable on its own, you need to eliminate the other numbers or terms associated with it. Starting from the equation \[ t + 6 = 43 \], we want to isolate \ t \ by removing the number \ 6 \ from the left side. Using the subtraction principle, subtract 6 from both sides.
This operation looks like this:
\[ t + 6 - 6 = 43 - 6 \]
Simplifying this, we remove the \ 6 \ on the left, leaving us with:
\[ t = 37 \]
Now, \ t \ is isolated, and we can see that \ t = 37 \.
verification of solutions
Verification is essential to ensure that the solution is correct. To verify \ t = 37 \, substitute \ 37 \ back into the original equation \[ t + 6 = 43 \]. Check if the left side equals the right side: \[ 37 + 6 = 43 \]. If both sides match, the solution is verified. This means the value we calculated for \ t \ is correct. Verification helps catch any errors and ensures your solution is accurate. It's a step that should never be skipped, as it confirms that your algebraic manipulations were performed correctly.

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