Three times the difference of a number and two is equal to the sum of the number and twelve.

x=-21

Step-by-step explanation:

The difference of a number and 3 is x - 3

The sum of the number and 5 is x + 5  

Twice the difference of a number and 3 is therefore 2(x - 3)  

Three times the sum of the number and 5 is therefore 3(x + 5)  

These last two terms are equal. In equation form this is:  

2(x - 3) = 3(x + 5)

2x - 6 = 3x + 15  

Get rid of the 3x on the right side by subtracting 3x from both sides and you have:  

-x - 6 = 15  

Get rid of the -6 on the left side by adding 6 to both sides to get:  

-x = 21  

You are trying to solve for +x. To change the left side of this equation to +x multiply

both sides by -1 and you change the equation to:  

x = -21

Hope this helps you to understand the problem.

step-by-step explanation:

she will travel a distance in the range of 3 - 11 miles