Certainly! Let's simplify the given expression step-by-step. The given expression is:
[tex]\[ -8y - (x - 4x) + 3y \][/tex]
### Step 1: Simplify Inside the Parentheses
First, simplify the expression inside the parentheses:
[tex]\[ x - 4x \][/tex]
This can be simplified by combining like terms (the [tex]\( x \)[/tex] terms):
[tex]\[ x - 4x = -3x \][/tex]
### Step 2: Substitute Back
Now substitute [tex]\( -3x \)[/tex] back into the original expression:
[tex]\[ -8y - (-3x) + 3y \][/tex]
### Step 3: Remove the Parentheses
Removing the parentheses, we need to remember that subtracting a negative is equivalent to adding the positive value:
[tex]\[ -8y + 3x + 3y \][/tex]
### Step 4: Combine Like Terms
Now, combine the like terms, which are the terms involving [tex]\( y \)[/tex]:
[tex]\[ -8y + 3y \][/tex]
Combining these gives us:
[tex]\[ -8y + 3y = -5y \][/tex]
### Step 5: Write the Final Expression
After combining the [tex]\( y \)[/tex] terms, the final expression is:
[tex]\[ -5y + 3x \][/tex]
Therefore, the simplified form of the given expression is:
[tex]\[ -5y + 3x \][/tex]
