Can you rewrite 10.5 as the difference of a product and a number?
Between 3 and 4.
Practice makes perfect
To approach the solution of this equation using mental math, we should think about how we could rewrite one side or the other to more closely match the other side. Let's try rewriting 10.5.
10.5=3n-1 ⇔ 11.5-1=3n-1
By rewriting 10.5 as 11.5-1, we made both sides of the equation look very similar. In fact, we can say that because there is a -1 on both sides of the equation, 11.5 must be equal to 3n, and we can disregard the -1 for now.
11.5 -1=3n -1 ⇒ 11.5=3n
With that in mind, maybe we can similarly rewrite 11.5 as a product of 3 and some number. There are two integer products of 3 that are close to 11.5, so the solution is between those two values. Let's test some numbers that, when multiplied by 3, are close to 11.5.
n
3n
Value
2
3 (2)
6
3
3 (3)
9
4
3 (4)
12
5
3 (5)
15
The solution to the given equation is between 3 and 4.
