Question

If the solution to the equation 14x 5 = 27x − 51 is x = where p and q are relatively prime p q positive integers, what is p q?

Answer 1

The simplified fraction is: x= 56/13 .​So, p=56 and q=13. The required answer is p/q=56/13.

Let's solve the given equation for x:

14x+5=27x−51

First, let's simplify the equation by moving all the terms involving x to one side of the equation and the constants to the other side:

14x−27x=−51−5

Combine like terms:

−13x=−56

Now, solve for x by dividing both sides by -13:

x= −56/−13

​To express this fraction in the form of p​/q where p and q are relatively prime positive integers.

we can simplify the fraction by finding the greatest common divisor (GCD) of 56 and 13.

The GCD of 56 and 13 is 1.

Therefore, the simplified fraction is:

x= 56/13