SKILL MAINTENANCE. Calculate:
2b + 8 – 3b = 10 + 11b – 2 – 12b
Your equation reduces to
-b + 8 = -b + 8
That is an identity.
b can be any number. You cannot "solve" for it.
always true
To solve the equation 2b + 8 - 3b = 10 + 11b - 2 - 12b, we first need to simplify both sides of the equation.
Let's start by combining like terms on both sides of the equation.
On the left-hand side of the equation:
2b - 3b
We can combine these terms by subtracting 3b from 2b, which gives us -b.
So, the left-hand side of the equation becomes: -b + 8.
On the right-hand side of the equation:
11b - 12b
We can combine these terms by subtracting 12b from 11b, which gives us -b.
So, the right-hand side of the equation becomes: 10 - 2 -b.
Now our equation becomes: -b + 8 = 10 - 2 -b.
To further simplify, let's combine the numbers on the right-hand side:
10 - 2 = 8.
Now our equation becomes: -b + 8 = 8 - b.
The equation now looks like this: -b + 8 = 8 - b.
Now, we want to get all the terms with "b" on one side of the equation, so let's add b to both sides:
-b + b + 8 = 8 - b + b.
Simplifying further, -b + b cancels out on the left-hand side, leaving us with:
8 = 8.
This equation is true regardless of the value of b.
So, the solution to the equation is that b can be any real number.
In summary, the solution to the equation 2b + 8 - 3b = 10 + 11b - 2 - 12b is that b can be any real number.