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Chapter 2: Problem 28

Solve each equation, and check your solution. $$ x+21.5=-13.4 $$

Short Answer

Expert verified
x = -34.9

Step by step solution

01

- Isolate the Variable

First, isolate the variable by subtracting 21.5 from both sides of the equation. This will help in getting the value of x.\[ x + 21.5 - 21.5 = -13.4 - 21.5 \]Simplify both sides:\[ x = -34.9\]
02

- Verify the Solution

To verify the solution, substitute the value of x back into the original equation:\[-34.9 + 21.5 = -13.4\]Simplify the left side:\[-13.4 = -13.4\]Since both sides of the equation 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
The first step in solving any linear equation is to isolate the variable. This means you want to get the variable, in this case, 'x', alone on one side of the equation.
For the given equation: x+21.5=-13.4,
we need to remove the constant term (21.5) from the left side. To do this, perform the same mathematical operation on both sides of the equation: subtract 21.5.
\(x + 21.5 - 21.5 = -13.4 - 21.5\).
Simplifying both sides gives us: x = -34.9. Now, the variable 'x' is isolated, and we have determined its value.
Check Your Solution
After finding the value of the variable, it's crucial to check your solution. This ensures that the obtained value satisfies the original equation.
Here's how you can verify it:
1. Start with the original equation: x + 21.5 = -13.4.
2. Substitute the isolated variable's value (-34.9) back into the equation:
\( -34.9 + 21.5 = -13.4\).
3. Simplify the left side to confirm both sides are equal. Since -34.9 + 21.5 indeed equals -13.4, the solution x = -34.9 is accurate.
Simplify Equations
When solving linear equations, simplifying expressions on both sides is a critical step. Breaking down complex expressions into simpler, manageable parts can help in solving the equation more efficiently.
Look at our example:\(x + 21.5 = -13.4\). By performing the subtraction: \(x = -34.9\), we simplify this equation.
Always aim to keep simplification steps clear and concise to avoid errors. Simplifying ensures each step is straightforward and the equation remains balanced, making other steps like isolating variables and checking solutions easier.

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