Solve:`0.3x+0.4=0.28x+1.16`

Options

A. `0.38`
B. `3.8`
C. 380
D. 38

Answer

To solve the equation \(0.3x + 0.4 = 0.28x + 1.16\), we will follow these steps:

### Step 1: Move all terms involving \(x\) to one side
We want to isolate \(x\) on one side of the equation. To do this, we will subtract \(0.28x\) from both sides:

\[ 0.3x - 0.28x + 0.4 = 1.16 \]

### Step 2: Simplify the equation
Now, we simplify the left side:

\[ (0.3 - 0.28)x + 0.4 = 1.16 \]

Calculating \(0.3 - 0.28\):

\[ 0.02x + 0.4 = 1.16 \]

### Step 3: Move the constant term to the other side
Next, we will subtract \(0.4\) from both sides:

\[ 0.02x = 1.16 - 0.4 \]

### Step 4: Simplify the right side
Calculating \(1.16 - 0.4\):

\[ 0.02x = 0.76 \]

### Step 5: Solve for \(x\)
Now, we will divide both sides by \(0.02\):

\[ x = \frac{0.76}{0.02} \]

### Step 6: Simplify the division
To make the division easier, we can multiply the numerator and the denominator by 100:

\[ x = \frac{0.76 \times 100}{0.02 \times 100} = \frac{76}{2} \]

Calculating \(76 \div 2\):

\[ x = 38 \]

### Final Answer
Thus, the solution to the equation \(0.3x + 0.4 = 0.28x + 1.16\) is:

\[ \boxed{38} \]

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