Solve the equations and check your answer in the case:
`0.6x-1.9=0.2x+0.5`

Answer

To solve the equation \(0.6x - 1.9 = 0.2x + 0.5\), we will follow these steps:

### Step 1: Rearrange the equation to isolate x terms on one side
We start with the equation:
\[ 0.6x - 1.9 = 0.2x + 0.5 \]

To isolate the x terms, we will subtract \(0.2x\) from both sides:
\[ 0.6x - 0.2x - 1.9 = 0.5 \]

### Step 2: Simplify the equation
Now, simplify the left side:
\[ (0.6 - 0.2)x - 1.9 = 0.5 \]
\[ 0.4x - 1.9 = 0.5 \]

### Step 3: Move the constant term to the right side
Next, we will add \(1.9\) to both sides to move the constant term:
\[ 0.4x = 0.5 + 1.9 \]

### Step 4: Simplify the right side
Now, simplify the right side:
\[ 0.4x = 2.4 \]

### Step 5: Solve for x
To find \(x\), divide both sides by \(0.4\):
\[ x = \frac{2.4}{0.4} \]

### Step 6: Calculate the value of x
Now, perform the division:
\[ x = 6 \]

### Step 7: Check the solution
To verify our solution, we will substitute \(x = 6\) back into the original equation:
Left side:
\[ 0.6(6) - 1.9 = 3.6 - 1.9 = 1.7 \]

Right side:
\[ 0.2(6) + 0.5 = 1.2 + 0.5 = 1.7 \]

Since both sides are equal:
\[ 1.7 = 1.7 \]

Thus, the solution is verified.

### Final Answer:
The value of \(x\) is \(6\).

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