For every positive 2-digit number, x, with tens digit t and units digit u , let y be the 2 digit number formed by reversing the digits of x. Which of the following expressions is equivalent to x-y?
a. 9(t-u) b. 9(u-t) c. 9t-u d.0
To find the expression equivalent to x-y, we first need to find the value of x and y. Let's say the tens digit of x is t and the units digit is u. Therefore, the value of x can be written as 10t + u.
Reversing the digits gives us y, which can be written as 10u + t.
Now, let's subtract y from x:
x - y = (10t + u) - (10u + t)
Simplifying this expression:
x - y = 10t + u - 10u - t
x - y = 9t - 9u
We can further factor out 9 from both terms:
x - y = 9(t - u)
Therefore, the expression equivalent to x-y is 9(t-u).
So, the correct answer is (a) 9(t-u).