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Chapter 5: Problem 326

In the following exercises, solve the equation. Then check your solution. $$ x-5=-11 $$

Short Answer

Expert verified
x = -6

Step by step solution

01

Isolate the variable

To solve for x, we need to isolate the variable on one side of the equation. Add 5 to both sides of the equation to get rid of the -5 on the left side.
02

Simplify the equation

After adding 5 to both sides, the equation becomes: \[ x - 5 + 5 = -11 + 5 \] Simplify to get: \[ x = -6 \]
03

Check the solution

Substitute \( x = -6 \) back into the original equation to verify it: \[ -6 - 5 = -11 \] This simplifies to: \[ -11 = -11 \], confirming the solution 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
When solving linear equations, the first step is usually isolating the variable. This means getting the variable by itself on one side of the equation. For example, starting with the equation: \[ x - 5 = -11 \] we need to remove the -5 attached to x. To do this, we perform the same operation on both sides of the equation to maintain balance. Here, we add 5 to both sides: \[ x - 5 + 5 = -11 + 5 \] This leaves us with \[ x = -6 \]. By isolating the variable, we simplify the equation and solve for x. It鈥檚 important to perform identical operations on both sides to keep the equation true.
Simplifying Equations
Simplifying equations is another key step in solving linear equations. After isolating the variable, you will typically need to simplify further by combining like terms or performing arithmetic operations. In the example given: \[ x - 5 + 5 = -11 + 5 \], combining the terms on both sides gives \[ x = -6 \]. Simplifying equations helps in reducing them to their simplest form, making it easier to solve for the variable. To simplify correctly, always ensure you follow the basic arithmetic rules and perform operations step-by-step.
Checking Solutions
After solving the equation, it's crucial to check the solution to verify its correctness. This involves substituting the found value back into the original equation to see if it satisfies the equation. For our solution \( x = -6 \), we substitute it back into the original equation: \[ -6 - 5 = -11 \]. This simplifies to \[ -11 = -11 \], confirming the solution is correct. Checking solutions helps to ensure there were no mistakes made during the isolating or simplifying steps. Always remember to perform this verification step to confirm your answer.

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