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 $\boxed{{\displaystyle 2.43}}$.