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Solving linear equations is like unraveling a mystery: you need to find the value of the unknown that makes the equation true. A common technique essential to this process is to isolate the variable. Imagine that the variable is a treasure you need to find, but it's buried and surrounded by numbers. To get to it, you'll need to eliminate everything around it.

Let's use the equation \( -5m = 20 \) as an example. Here, the treasure is \( m \) and is multiplied by \( -5 \). To isolate \( m \) and discover its value, we must remove the \( -5 \) by performing the opposite operation. Since \( m \) is being multiplied by \( -5 \) you'll divide by \( -5 \) on both sides of the equation. This balancing act results in \( m = -4 \), and voilà, you've isolated the variable and uncovered the treasure!

Once we've predicted the value of our variable, to ensure we're not led astray by a false lead, we must verify our find using the substitution method. This is akin to double-checking the map after you've found the location to confirm it's the right spot.

In the example of \( m = -4 \), we place it back into the original equation in place of \( m \). Think of it as retracing your steps to make sure you followed the map correctly. Substituting \( -4 \) for \( m \) in \( -5m = 20 \) gives us \( -5(-4) = 20 \)—which simplifies to \( 20 = 20 \)—verifying that our solution is indeed the treasure we were looking for.

The last step in the journey of solving linear equations is equation checking. Think of it as marking the spot on the map with a permanent 'X,' signifying a successful expedition. Equation checking ensures that the solution we've found doesn't just look good on paper but actually 'solves' the equation — making both sides equal.

For the equation \( -5m = 20 \) with the solution \( m = -4 \), we see that when we substitute \( -4 \) back in, we should get a true statement. By simplifying the substituted equation and seeing that indeed, \( 20 = 20 \) after all our operations, we can confidently claim our solution \( -4 \) is correct. Equation checking is our assurance that no math rule has been broken and every step has been followed accurately, concluding our treasure hunt triumphantly.