91Ó°ÊÓ

To solve the linear equation \(-0.5x = 20\), the first step is to isolate the variable. In this equation, our variable is \(x\).
Isolating the variable means we want \(x\) to be by itself on one side of the equation.
This way, we can find its value easily.

To do this, we look at what actions are being performed on \(x\).
In this case, \(x\) is being multiplied by \(-0.5\).
To isolate \(x\), we need to undo this multiplication.

The opposite of multiplication is division.
Therefore, we will divide both sides of the equation by \(-0.5\). By dividing both sides, we ensure that the equality is maintained and effectively cancel out the multipliers on \(-0.5x\).
Here’s what it looks like:
\[ -0.5x = 20 \]
Divide both sides by \(-0.5\):
\[ x = \frac{20}{-0.5} \]

Now that we have the equation \(\frac{20}{-0.5}\), it’s time to carry out the division.
Division in algebra works similarly to how it does with regular numbers.
To divide by a fraction or a decimal, you can think of it as multiplying by its reciprocal.
In this case, dividing by \(-0.5\) is the same as multiplying by \-2\:.

Think about it as:

• \[ x = 20 \times -2 \]

When you perform this multiplication, you get:

\[ x = -40 \]
Now, you have found the value of \x\. It’s \-40\.

Once we have the value of \ x\, the last step is to check our solution.
Checking solutions is important because it verifies our work.
To do this, we substitute the value of \ x\ back into the original equation.

Remember the original equation:
\[ -0.5x = 20 \]
Substitute \ x = -40 \:
\[ -0.5(-40) = 20 \]
Perform the multiplication:

\[ 20 = 20 \]
Both sides of the equation match!
This confirms that our solution is correct, and \( x = -40 \) is indeed the right answer.

Now you know how to solve linear equations by isolating the variable, using division, and checking your solutions.
This systematic approach will help you tackle many algebra problems with confidence.