translate this expression into a mathematical problem
the difference between one more than three times a number and a number is 19 find the smaller number
| (3 n +1) - n | = 19
note difference can be + or -
if +
2 n = 18
n = 9
if -
-2n = 18
n = -9
oops. |2n+1| = (2n+1) or -(2n+1)
if -(2n+1) = 19
-2n = 20
n = -10
check:
|(3(-10)+1-(-10)| = |-30+1+10| = |-19| = 19
To translate this expression into a mathematical problem, we need to assign a variable to represent the unknown number. Let's call that variable "x".
According to the given expression, the difference between one more than three times a number and the number is 19.
We can break down this expression into two parts:
1) Three times a number: 3x
2) One more than three times a number: 3x + 1
The difference between one more than three times a number and a number is 19. Mathematically, this can be represented as:
(3x + 1) - x = 19
Now we can solve this equation to find the value of "x" which represents the smaller number:
(3x + 1) - x = 19
Simplifying the equation, we have:
2x + 1 = 19
Subtracting 1 from both sides:
2x = 18
Dividing both sides by 2:
x = 9
Therefore, the smaller number is 9.