SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

Provide an appropriate response.
Identify an integer x for which 3x/4 represents a ratio greater than 3 : 1 but less than 4 : 1.

Make a table

x 3x/4
3 2.25
4 3
5 3.75
6 4.5
Which x (integer) would you choose?

To find an integer x that satisfies the given condition, we need to compare the ratio 3x/4 with the ratios 3:1 and 4:1.

Let's convert the ratios to the same denominator by multiplying both sides by 4.

For the ratio 3:1, we have 3/1 = 12/4.
For the ratio 4:1, we have 4/1 = 16/4.

Now we know the range of values we are looking for is between 12/4 and 16/4. This means we need to find an integer x such that 3x/4 lies between these two fractions.

Taking the fraction 3x/4, we can rewrite it as a decimal by dividing 3x by 4.

So we need to find an integer x for which the decimal value of 3x/4 is greater than 3 and less than 4.

One possible approach is to consider integers starting from x = 2 and increase sequentially until we find a value that satisfies the condition.

Let's calculate the values for 3x/4:

For x = 2: (3 * 2)/4 = 6/4 = 1.5
For x = 3: (3 * 3)/4 = 9/4 = 2.25
For x = 4: (3 * 4)/4 = 12/4 = 3
For x = 5: (3 * 5)/4 = 15/4 = 3.75
For x = 6: (3 * 6)/4 = 18/4 = 4.5

From the calculations, we can see that for x = 4, the value of 3x/4 is exactly 3, which is on the lower end of our desired range. Therefore, x = 4 is the integer that satisfies the condition.