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Combining like terms is a crucial step in solving linear equations. Like terms are terms that have the same variable raised to the same power, although they can have different coefficients. Here's what it means to combine them:

When you see an equation like \(-5x + 4x - 8x = 0\), each term contains the variable \(x\). To combine them, you simply add or subtract their coefficients:

- First, take \(-5x\) and \(4x\), and add their coefficients: \(-5 + 4\), which equals \(-1\). So, you get \(-x\).
- Next, combine \(-x\) with \(-8x\). The coefficients are \(-1\) and \(-8\), which add up to \(-9\).
- This simplifies the equation to \(-9x = 0\).

Combining like terms makes the equation simpler and easier to solve. This step is foundational because it reduces the complexity of the equation.

Once you've combined like terms, the next step is isolating the variable. This means getting the variable by itself on one side of the equation. Here's how you can do it:

- In the equation \(-9x = 0\), you need to isolate \(x\).
- To do that, divide both sides of the equation by \(-9\) to keep the equation balanced:

\(\frac{-9x}{-9} = \frac{0}{-9}\)

- Simplifying this, you get \(x = 0\).

Isolating variables is key to finding their values. By isolating \(x\), you find what value of \(x\) makes the equation true. Always make sure to do the same operation to both sides of the equation to maintain balance.

After isolating the variable and finding the solution, it's essential to verify it. Verifying solutions ensures that your solution is correct. Here's how to do it:

- Substitute \(x = 0\) back into the original equation \(-5x + 4x - 8x = 0\).

- Replace every occurrence of \(x\) with \(0\):

\(-5(0) + 4(0) - 8(0) = 0\)

- Simplify each term:

\(0 + 0 + 0 = 0\)

- As both sides of the equation are equal, your solution \(x = 0\) is verified.

Verification is a final and crucial step in solving equations. It checks your work and confirms that the solution you found correctly satisfies the original equation. Always verify to avoid mistakes.