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When it comes to solving equations, the undoing process is all about reversing operations to simplify equations. Think of it like unwinding a series of mathematical actions to make a path towards the solution, step by step. For instance, let's take the equation \[-15 = -52 + 1.6x\]. Here, our job is to undo whatever is done to the variable, starting with addition or subtraction, and then, multiplication or division.
To tackle this:

• You first nullify the addition or subtraction near the variable by performing the opposite operation on both sides of the equation. For example, add 52 to both sides to counteract the \(-52\).
• Next, manage multiplication or division, typically by doing the opposite. Divide both sides by 1.6 to isolate \(x\).

The idea is that each step takes you closer to isolating the variable by repeatedly 'undoing' operations done around it. This simplifies everything until you find the value of the variable.

Equation verification is like a double-check to ensure your solution truly works. After finding what \(x\) or another variable equals using the undoing process, substitute this back into the original equation.
This is crucial because it shows whether the solution makes the original equation true.
Consider the earlier example: with equation (a), once you find \(x = 23.125\), substitute it back: \(-15 = -52 + 1.6 imes 23.125\). Calculating this, if both sides end up matching, you have correctly solved for \(x\). If they don't, it's a hint to revisit your steps and see where a mistake might have sneaked in.
Verification acts like a safety net, confirming your solution holds up under scrutiny, and reinforces your understanding of the steps involved in solving the equation.

The goal in solving an equation is often to isolate the variable, making it the star of its own stage without interference.
Once isolated, the variable reveals its value which solves the equation.
To isolate the variable efficiently:

• Identify what operations are surrounding the variable - this might be addition, subtraction, multiplication, or division.
• Each operation needs to be undone in the most straightforward way possible. Always perform the opposite operation to both sides of the equation at each step.
• Be systematic and patient - it often requires more than one step to fully isolate a variable.

When executed correctly, the variable will stand alone on one side, and that's half the battle won in equation-solving. From there, you're just a few straightforward steps away from uncovering its actual value.