What’s six less than twice a number is the same as the number increased by seven

First thing's first we need to figure out an equation to solve the problem. Let's call our mystery number "x." 

First, I'll examine the first part of the problem. "Six less than twice a number..." Well, we know that twice a number is our number multiplied by 2. In other words, 2x. Less than indicates that we must subtract. So the first expression is 2x-6. 

To say that this expression is the same as another is to say that they are equal. So now we have 2x-6= The second expression is seven less than x, or x-7.

Setting that equal to our first expression, we get 2x-6=x-7. Now we can solve for x.

2x-x-6=-7
x-6=-7
x=-7+6
x=-1

Our number is -1! Plug it back in to the original equation we made to double check.