Simplify the Expression: x-(3x+4y) Using Algebraic Properties

The negative sign in front of the parentheses acts like multiplying by -1. Since $-1 \times (+4y) = -4y$, the 4y becomes negative even though it was positive inside.

The parentheses make a huge difference! x-3x+4y gives you $-2x+4y$, but x-(3x+4y) gives you $-2x-4y$. The parentheses change the sign of everything inside.

Think of the negative as -1 multiplying the entire expression. Write it as $x + (-1)(3x+4y)$ to see that -1 multiplies both 3x and 4y!

Absolutely! Try x=2, y=1. Original: $2-(3 \cdot 2+4 \cdot 1) = 2-10 = -8$. Your answer: $-2(2)-4(1) = -4-4 = -8$ ✓

The same rule applies! The negative sign distributes to every single term inside the parentheses, no matter how many there are. Each positive becomes negative, and each negative becomes positive.