91Ó°ÊÓ

When solving linear equations, your first goal is to isolate the variable. This means you want the variable (like \(x\)) to be by itself on one side of the equation. To do this, you need to get rid of any coefficients or constants attached to the variable.
In our example, the equation is \(-0.5x = 20\). The variable here is \(x\), and its coefficient is -0.5. To isolate \(x\), we need to divide both sides of the equation by -0.5:
\[ \frac{-0.5x}{-0.5} = \frac{20}{-0.5} \]
This removes the -0.5 from the left side, leaving just \(x\). Now the equation looks like:
\[ x = \frac{20}{-0.5} \].
Isolating the variable is often the first step in solving an equation, and it sets you up for the next step: simplifying the sides.

Once the variable is isolated, the next step is to simplify the equation. Simplifying the equation helps to break it down into an easily understandable form.
In our example, we already have it down to:
\[ x = \frac{20}{-0.5} \]
Now, we perform the division on the right side.
20 divided by -0.5 equals -40, so our simplified equation is:
\[ x = -40 \].
Remember, simplifying equations involves basic arithmetic operations like addition, subtraction, multiplication, or division to make the equation cleaner. Always ensure you perform the same operations on both sides of the equation to maintain equality.

After solving an equation, it's important to verify your solution. Verifying ensures that the solution you found is correct.
To verify, substitute the solution back into the original equation. In our example, we found that \(x = -40\). Let's plug it back into the original equation:
Original equation: \(-0.5x = 20\)
Substitute \(x = -40\):
\[ -0.5(-40) = 20 \]
Simplify the left side:
\[ 20 = 20 \]
Both sides of the equation are equal, confirming that our solution \(x = -40\) is correct.
Verification is a critical step in problem-solving as it not only checks your work but also boosts your confidence in the accuracy of your solution.