Katy is between Houston and San Antonio. If the distance from Katy to San Antonio is 2 x x  5 miles and the distance from Katy to Houston is 4 12 x  miles. The total distance from Houston to San Antonio is 120 miles . Then How far is it between each City?

It is hard to read what you actually wrote, but i guess this is:

Distance to San Antonio = 2*5*x mi

Distance to Houston = 4*12*x mi

Distance from Houston to San Antonio = 120mi

Then we must have that:

2*5*x mi + 4*12*x mi = 120mi

(2*5 + 4*12)*x mi = 120mi

(10 + 48)*x mi = 120mi

x mi =120/58 mi = 2.06 mi

Now we can replace it in the above equations:

Distance to San Antonio = 2*5*2.06 mi = 20.6 mi

Distance to Houston = 4*12*2.06 mi =  98.88 mi

answer: solve 5\cdot 2^x=2405⋅2  

x

=2405, dot, 2, start superscript, x, end superscript, equals, 240.

solution

to solve for xxx, we must first isolate the exponential part. to do this, divide both sides by 555 as shown below. we do not multiply the 555 and the 222 as this goes against the order of operations!

\begin{aligned} 5\cdot 2^x& =240 2^x& =48 \\ \end{aligned}  

5⋅2  

x

2  

x

​    

=240

=48

​

step-by-step explanation: