Solve the following equation for x. Round the answer to the nearest hundredth.

Question

0.6(10x + 20) = 2.8(0.2x + 5)

A.
0.30
B.
0.37
C.
2.57
D.
2.72

Answer 1

To solve the equation \( 0.6(10x + 20) = 2.8(0.2x + 5) \), we will first distribute the constants on both sides.

1. Start with the left side: \[ 0.6(10x + 20) = 0.6 \cdot 10x + 0.6 \cdot 20 = 6x + 12 \]

2. Now, distribute on the right side: \[ 2.8(0.2x + 5) = 2.8 \cdot 0.2x + 2.8 \cdot 5 = 0.56x + 14 \]

Now, we have the equation: \[ 6x + 12 = 0.56x + 14 \]

3. Next, we want to get all the \( x \) terms on one side and the constant terms on the other side. Subtract \( 0.56x \) from both sides: \[ 6x - 0.56x + 12 = 14 \]

This simplifies to: \[ 5.44x + 12 = 14 \]

4. Now, subtract \( 12 \) from both sides: \[ 5.44x = 2 \]

5. Finally, divide both sides by \( 5.44 \) to solve for \( x \): \[ x = \frac{2}{5.44} \]

Calculating: \[ x \approx 0.3676 \]

Rounding to the nearest hundredth, we get: \[ x \approx 0.37 \]

Thus, the answer is B. 0.37.