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

Question

0.7(10x + 11) = 4.5(0.2x + 5)

A.
3.69
B.
0.41
C.
1.87
D.
2.43

Answer 1

To solve the equation \(0.7(10x + 11) = 4.5(0.2x + 5)\), we will first expand both sides:

1. Expand the left side: \[ 0.7(10x + 11) = 0.7 \times 10x + 0.7 \times 11 = 7x + 7.7 \]

2. Expand the right side: \[ 4.5(0.2x + 5) = 4.5 \times 0.2x + 4.5 \times 5 = 0.9x + 22.5 \]

Now we have the equation: \[ 7x + 7.7 = 0.9x + 22.5 \]

Next, we will isolate \(x\) by first subtracting \(0.9x\) from both sides: \[ 7x - 0.9x + 7.7 = 22.5 \] \[ 6.1x + 7.7 = 22.5 \]

Next, subtract \(7.7\) from both sides: \[ 6.1x = 22.5 - 7.7 \] \[ 6.1x = 14.8 \]

Finally, divide both sides by \(6.1\) to get \(x\): \[ x = \frac{14.8}{6.1} \approx 2.4262 \]

Rounding to the nearest hundredth, we find: \[ x \approx 2.43 \]

Thus, the answer is \( \boxed{2.43} \).