91Ó°ÊÓ

To solve a linear equation, the goal is often to find the value of the variable. This process is called isolating the variable. In our original exercise, we wanted to determine the value of \( d \).

First, we had the equation: \[ d - (-6) = -26 \].

We simplified this to \( d + 6 = -26 \).

Next, to isolate \( d \), we needed to get rid of the 6 added to \( d \). We did this by subtracting 6 from both sides of the equation:

\[ d + 6 - 6 = -26 - 6 \]

Mathematically, what you do to one side of the equation, you must do to the other to keep it balanced. After subtraction, the equation simplified to:

\[ d = -32 \]

And just like that, we found our variable isolated with the value \( -32 \). Isn't that straightforward and simple?

Simplification makes it easier to solve equations. When given a problem like \( d - (-6) = -26 \), the first thing to do is simplify the terms.

Remember, subtracting a negative number is the same as adding its positive counterpart. So, \( d - (-6) \) becomes \( d + 6 \).

This simplifies our equation to:

\[ d + 6 = -26 \]

With simpler terms, it's easier to see the next step: isolating the variable. Keep in mind, simplifying doesn't change the equation's meaning; it only makes it easier to understand and solve.

Negative numbers are essential in algebra, and understanding how to work with them is key in solving equations.

Subtracting a negative number, as in our original equation \( d - (-6) \), might seem tricky at first. But, recall that subtracting a negative is the same as adding the positive counterpart. So, \( d - (-6) \) becomes \( d + 6 \).

Here's a quick refresher:

• \( -(-A) = +A \)
• \( -A + (-B) = -(A+B) \)

These simple rules help navigate through more complex problems with confidence.

In our exercise, once we understood subtracting \(-6\) is the same as adding \(6\), the rest of the problem became straightforward. Understanding negative numbers simplifies the process of solving equations.