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When solving mathematical problems, especially equations, simplifying is often the first and most crucial step. Simplification involves reducing an equation to its most basic form, making it easier to understand and solve. In our example, the equation is \(x-(-6)=8\). The presence of a double negative can initially make the equation appear confusing.

To simplify the equation, we must recognize mathematical rules that help in transforming the equation into a simpler form. Recognizing a double negative is one such rule, which is key to simplifying this particular equation. Transforming the double negative, we convert \(-(-6)\) into +6, simplifying our equation to \(x+6=8\). This step removes any confusion that the double negative might cause and eases the process of solving for the variable.

Addressing the concept of a double negative is essential in understanding how to simplify equations. In math, just like in grammar, two negatives make a positive. When you come across expressions like \(-(-6)\), it's important to realize that they simplify to +6. This happens because negating a negative value switches its polarity, resulting in a positive.

• Remember: \(-(-x) = +x\) for any number x.
• Application: In our exercise, \(-(-6)\) became +6, simplifying the equation to \(x+6=8\).

Recognizing and resolving double negatives is an essential skill when simplifying equations since it helps avoid errors and misunderstandings in further solution steps.

To find the solution to an equation, isolating the variable on one side of the equation is an important process. The variable, typically represented by a letter such as \(x\), is what we need to solve for. This process involves performing operations to both sides of the equation that will eventually leave the variable on one side and a numerical value on the other.

For our problem, once we simplified the equation to \(x+6=8\), we needed to isolate \(x\). We did this by subtracting 6 from both sides of the equation, which maintains the balance of the equation: \(x+6-6 = 8-6\). This simplification results in \(x = 2\) since subtracting 6 from both sides leaves the variable alone on one side.

Key Actions When Isolating a Variable:

• Add or subtract the same number from both sides to cancel additional terms.
• Multiply or divide both sides by the same number to deal with coefficients attached to the variable.