Select the correct answer. Simplify the following expression. \[ (38 x+61 y)-(3 x-11 y) \] \( 35 x-50 y \) \( 41 x+50 y \) \( 41 x-72 y \) \( 35 x+72 y \)

To simplify the expression \((38 x + 61 y) - (3 x - 11 y)\), start by distributing the negative sign across the second set of parentheses. This gives us: \[ 38 x + 61 y - 3 x + 11 y \] Now, combine like terms: \[ (38 x - 3 x) + (61 y + 11 y) = 35 x + 72 y \] So, the simplified expression is \(35 x + 72 y\). The correct answer is \(35 x + 72 y\). --- In the world of algebra, simplifying expressions like this one is a fundamental skill! It's like tidying up your room—you're just making everything neat and in its place, which makes it clearer to see what you have. If you're ever confused, remember to carefully deal with the signs when you distribute them. A common mistake is forgetting that subtracting a negative is like adding a positive! Keeping track of your signs can save you from a lot of headaches.