Solve the following equations.Check your result in each case
`0.5x-(0.8-0.2x)=0.2-0.3x`

Answer

To solve the equation \(0.5x - (0.8 - 0.2x) = 0.2 - 0.3x\), we will follow these steps:

### Step 1: Distribute the negative sign
Start by distributing the negative sign across the terms in the parentheses on the left side of the equation.

\[ 0.5x - 0.8 + 0.2x = 0.2 - 0.3x \]

### Step 2: Combine like terms
Now, combine the like terms on the left side of the equation.

\[ (0.5x + 0.2x) - 0.8 = 0.2 - 0.3x \]

This simplifies to:

\[ 0.7x - 0.8 = 0.2 - 0.3x \]

### Step 3: Move all x terms to one side
Next, we will move all the terms involving \(x\) to one side of the equation and the constant terms to the other side. We can add \(0.3x\) to both sides:

\[ 0.7x + 0.3x - 0.8 = 0.2 \]

This simplifies to:

\[ 1.0x - 0.8 = 0.2 \]

### Step 4: Move the constant term to the other side
Now, add \(0.8\) to both sides to isolate the \(x\) term:

\[ 1.0x = 0.2 + 0.8 \]

This simplifies to:

\[ 1.0x = 1.0 \]

### Step 5: Solve for x
Now, divide both sides by \(1.0\):

\[ x = 1 \]

### Step 6: Check the result
To verify our solution, we will substitute \(x = 1\) back into the original equation:

**Left Side:**
\[ 0.5(1) - (0.8 - 0.2(1)) = 0.5 - (0.8 - 0.2) = 0.5 - 0.6 = -0.1 \]

**Right Side:**
\[ 0.2 - 0.3(1) = 0.2 - 0.3 = -0.1 \]

Since both sides are equal, our solution is verified.

### Final Answer:
\[ x = 1 \]