The absolute value
returns the "positive version" of a number.
In other words, if the number is positive, it remains positive; if the number is negative, it changes sign.
So, if we want
, we want the "positive version" of x to be 9.
This can happen in two ways: if x is already 9, then its absolute value is still nine. If instead x=-9, its positive value will be 9 again.
In formula, we have

because

To solve for j, cross multiply:
4 x 45 = 18 x j
180 = 18j
Divide both sides by 18:
j = 10
Answer:
The smallest positive integer solution to the given system of congruences is 30.
Step-by-step explanation:
The given system of congruences is


where, m and n are positive integers.
It means, if the number divided by 5, then remainder is 0 and if the same number is divided by 11, then the remainder is 8. It can be defined as



Now, we can say that m>n because m and n are positive integers.
For n=1,


19 is not divisible by 5 so m is not an integer for n=1.
For n=2,



The value of m is 6 and the value of n is 2. So the smallest positive integer solution to the given system of congruences is

Therefore the smallest positive integer solution to the given system of congruences is 30.
Answer:
One of it culd be -3 or 3
Step-by-step explanation: