How many solutions does 6 - 3x = 12 - 6x have?

1 solution

Step-by-step explanation:

Remark

1 solution

Rule: the number of solutions to an equation is at most the same number as the highest number on the variable. for example

x^3 + 4x^2 - 6x - 15 has at most 3 real solutions because the highest power is x^3

x^n + x^ (n - 1) ... has at most n real solutions. It can have fewer.

Solution

So 6 - 3x = 12 - 6x Subtract 6 from both sides

6 - 6 - 3x = 12 - 6 - 6x Combine

-3x = 6 - 6x Add 6x to both sides

-3x + 6x = 6 Combine

3x = 6 Divide by 3

x = 6/3 = 2

Check

6 - 3 (2) = 12 - 6 (2)

0 = 0 which checks