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Chapter 2: Problem 13

\(x-6=-9\)

Short Answer

Expert verified
x = -3

Step by step solution

01

Identify the equation

The given equation is: \(x-6=-9\)
02

Add 6 to both sides

To isolate the variable \(x\), add 6 to both sides of the equation: \(x-6+6=-9+6\)
03

Simplify both sides

Simplifying both sides, we get: \(x=-3\)

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Key Concepts

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

Isolate the Variable
One of the key steps to solving linear equations is isolating the variable. To isolate a variable means to get the variable by itself on one side of the equation. This often involves undoing whatever operations are currently performed on the variable.
For the equation given in the exercise, \(x-6=-9\), the variable 'x' is not yet isolated because it is being subtracted by 6. To isolate 'x', we need to remove the -6 by performing the opposite operation, which is addition.
By adding 6 to both sides, as shown: \(x-6+6=-9+6\), we can cancel out the -6 on the left side, leaving the variable 'x' alone. This single step brings us significantly closer to the solution!
Simplifying Equations
Once we've performed the same operation on both sides of the equation, we need to simplify it. Simplifying just means making the equation as straightforward as possible.
In our exercise, after we added 6 to both sides, we got the new equation: \(x-6+6=-9+6\). This simplification removes the -6 and the +6 on the left side: \(x=-3\).
Simplification is crucial because it reduces the complexity of the equation, paving the way for easier interpretation and solving. Always remember that the goal is to have the variable alone on one side.
Basic Algebra Steps
Understanding the basic steps of algebra helps in solving almost any linear equation. The sequence typically follows a pattern, which if mastered, makes algebra straightforward. Here are the basic steps:
  • Identify the equation.
  • Isolate the variable by using inverse operations.
  • Simplify both sides of the equation after performing the operation.
  • Check your solution by substituting it back into the original equation.
In our given problem, we first identified the equation \(x-6=-9\). We then isolated the variable by adding 6 to both sides. Finally, we simplified to get \(x=-3\).
Following these steps systematically ensures that you arrive at the correct solution methodically and efficiently. Always practice these fundamental steps to become comfortable with basic algebra.

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