Alright! Let's solve the equation step by step.
Given equation:
[tex]\[ y - 3 = -3y - 43 \][/tex]
### Step 1: Simplify both sides of the equation
We start by simplifying the equation in order to make it easier to solve.
To do this, we want to get all terms involving [tex]\( y \)[/tex] on one side of the equation, and all constant terms on the other side.
### Step 2: Move all terms involving [tex]\( y \)[/tex] to one side
We'll add [tex]\( 3y \)[/tex] to both sides of the equation to move the [tex]\( -3y \)[/tex] term to the left side.
[tex]\[ y - 3 + 3y = -3y - 43 + 3y \][/tex]
This simplifies to:
[tex]\[ y + 3y - 3 = -43 \][/tex]
### Step 3: Combine like terms
Now, combine the [tex]\( y \)[/tex] terms on the left side.
[tex]\[ 4y - 3 = -43 \][/tex]
### Step 4: Isolate the variable term
To isolate the [tex]\( 4y \)[/tex] term, we'll add 3 to both sides of the equation.
[tex]\[ 4y - 3 + 3 = -43 + 3 \][/tex]
This simplifies to:
[tex]\[ 4y = -40 \][/tex]
### Step 5: Solve for [tex]\( y \)[/tex]
To solve for [tex]\( y \)[/tex], we'll divide both sides of the equation by 4.
[tex]\[ \frac{4y}{4} = \frac{-40}{4} \][/tex]
[tex]\[ y = -10 \][/tex]
### Final Solution
The solution to the equation [tex]\( y - 3 = -3y - 43 \)[/tex] is:
[tex]\[ y = -10 \][/tex]
This means when you substitute [tex]\( y = -10 \)[/tex] back into the original equation, both sides will be equal, confirming that the solution is correct.
Therefore, the detailed step-by-step solution to the equation [tex]\( y - 3 = -3y - 43 \)[/tex] is:
[tex]\[ y = -10 \][/tex]
