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Chapter 3: Problem 8

Solve the equation. $$8+h=0$$

Short Answer

Expert verified
The solution is \( h = -8 \).

Step by step solution

01

- Isolate the Variable

To solve for the variable, subtract 8 from both sides of the equation: Equations: - : To solve the equation To isolate -8 = 0 - 8 - = To isolate the variable h, subtract it from both sides = - : equation, subtract 8 from both sides. this side =8
02

- Simplify the Equation

Simplify both sides of the equation: \[h = -8\]
03

- Solution Verification

To verify the solution, substitute \(h\) back into the original equation to check if it holds true: \[8 + (-8) = 0\]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.

Isolate the Variable
When solving linear equations, the goal is to find the value of the unknown variable. To do this, we need to isolate the variable on one side of the equation. In the equation \(8 + h = 0\), we want to get \(h\) by itself.

To isolate the variable \(h\), we need to eliminate the constant term from the left side of the equation. This can be done by subtracting 8 from both sides. In mathematical terms, this is represented as:

\[8 + h - 8 = 0 - 8\]

On the left side, the 8s cancel each other out, leaving:

\[h = -8\]
This process of isolating the variable allows us to see that \(h = -8\).
Simplify Equations
The next step after isolating the variable is to simplify the equation, if necessary. Simplification means performing any arithmetic operations or combining like terms to ensure the equation is in its simplest form.

In our example, the equation \(h = -8\) is already simplified because it clearly shows the value of the variable \(h\). There are no additional steps needed in terms of arithmetic operations.

This shows that simplifying an equation helps in making the solution more straightforward and easy to understand.
Solution Verification
After finding the value of the variable, it's important to verify the solution to ensure it's correct. Verification involves substituting the found value back into the original equation and checking if both sides of the equation are equal.

For the equation \(8 + h = 0\), we substitute \(h = -8\) back into the equation:

\[8 + (-8) = 0\]

Performing the addition gives:

\[0 = 0\]

Since both sides of the equation are equal, this confirms that our solution \(h = -8\) is correct. Always verifying your solutions ensures accuracy and reinforces your understanding of the problem.

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