9. a three-digit number, xyz, is formed of three different non-zero digits x , y , and z. a new number is formed by rearranging the same three digits. what is the greatest possible difference between the two numbers? (for ex- ample, 345 could be rearranged into 435, for a difference of 435 - 345

An equation in which there is only one variable is known as a linear equation in one variable.
It has the mathematical formula Ax + B = 0, where A and B can be any two real numbers, and x is an unknowable variable with just one possible value.
One such linear equation in one variable is 9x + 78 = 18.

Let m be the digit from 2 to 8.

The larger three digit number will look like 9m1, while the smaller three digit number will look like 1m9.

Assume a three digits number lets say 189.

Then the largest possible three digit number after rearranging above number is 981.

981 - 189 = 792

Again assume a three digits number lets say 149.

Then the largest possible three digit number after rearranging above number is 941.

941 - 149 = 792

for m their difference is constant i.e:792, which is the highest possible difference.

Learn more about linear equation

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