A hiking trail is 2.4 miles long. Two hikers walked 2 2/8 miles along the trail. Did they walk the entire trail? Explain your thinking. (Please give step by step math)

They did not walk the entire trail.

Step-by-step explanation:

We can first convert 2.4 to a fraction.

(List of decimal places to make the explanation easier to follow)

.0 - tenths

.00 - hundredths

.000 - thousandths

We can split 2.4 into 2+0.4

Start by converting 0.4...

Since the "4" is in the tenths place this means that the fraction would be 4/10.

We can simplify this by dividing 4/10 by 2/2. Notice we can only do this because 2/2 is equivalent to one, so in a sense we are only dividing the fraction by 1.

Now we add the 2 back on to get...

2 2/5

We can turn it into an improper fraction (multiply the first "large" number by the denominator of the fraction and then add the numerator)

12/5

Now, convert the second fraction...

18/8

We can simplify this by again dividing the fraction by 2/2...

9/4

Now we compare which is greater using the cross multiplication method (numerator of the first fraction multiplied by denominator of the second fraction and numerator of the second fraction multiplied by the denominator of the first fraction):

12*4

9*5

48>45

Therefore 12/5 is greater meaning the hikers did not walk the entire trail

x =±sqrt(1/3)

step-by-step explanation:

x+4/6x=1/x

multiply each side by 6x to get rid of the fractions

6x*(x+4/6x)=1/x*6x

distribute

6x^2 +4 = 6

subtract 4 from each side

6x^2 +4-4 = 6-4

6x^2 =2

divide by 6

6x^2/6 = 2/6

x^2 = 1/3

take the square root of each side

sqrt(x^2) = ±sqrt(1/3)

x =±sqrt(1/3)