2(x-8)+x=3(x-6)+2
2x-16+x=3x-18+2
3x-16=3x-16
so the equation makes no sense
x=0
It is identity. Any value would fit.
To solve this equation, we need to simplify and isolate the variable x.
Let's start by distributing the terms on both sides of the equation:
2(x-8) + x = 3(x-6) + 2
Apply the distributive property:
2x - 16 + x = 3x - 18 + 2
Combine like terms:
3x - 16 = 3x - 16
Now, we notice that the variable x appears on both sides of the equation. In this case, we can subtract 3x from both sides to eliminate the variable:
3x - 16 - 3x = 3x - 16 - 3x
Simplifying:
-16 = -16
At this point, we find that both sides of the equation are equal. This means that the equation is true for any value of x. Therefore, the solution to this equation is all real numbers, or in algebraic notation, it can be written as x ∈ ℝ.
In other words, any value you substitute for x in the original equation will satisfy the equation.