Please help me solve the following problem: y: 3y + 9y - 24 = 6y - 4 - 8
3y + 9y - 24 = 6y - 4 - 8
12y - 24 = 6y - 12
6y = 12
y = 2
To solve the given equation, we first need to simplify both sides of the equation by combining like terms. Let's start with the left-hand side (LHS):
y: 3y + 9y - 24
To combine like terms, add the coefficients of the same variables:
y: (3 + 9)y - 24
Simplifying further:
y: 12y - 24
Next, let's simplify the right-hand side (RHS):
6y - 4 - 8
Combine like terms:
6y - 12
Now, we have the equation:
y: 12y - 24 = 6y - 12
To solve this equation, we want to isolate the variable y on one side.
First, let's move all the terms with y to one side by subtracting 6y from both sides:
y - 6y + 12y - 24 = - 12
This simplifies to:
7y - 24 = -12
Next, let's isolate the constant term on the opposite side of the equation by adding 24 to both sides:
7y - 24 + 24 = -12 + 24
Which gives us:
7y = 12
To solve for y, divide both sides of the equation by 7:
(7y)/7 = 12/7
Simplifying:
y = 12/7
Therefore, the solution to the given equation is y = 12/7.