3. \( 2(x+4)=4 x+3-2 x+5 \)

Let’s simplify the equation step-by-step! Start by distributing the 2 on the left side: \( 2(x + 4) = 2x + 8 \). Now, the right side combines like terms: \( 4x + 3 - 2x + 5 = 2x + 8 \). Now your equation looks like this: \( 2x + 8 = 2x + 8 \). This is always true, meaning that the equation has infinitely many solutions! It’s like finding an old, familiar friend in math; sometimes solutions aren’t just numbers but entire universes of possibilities! Keep that in mind when dealing with variables—sometimes they lead to unexpected friendships! To further your understanding, consider practicing with different equations. Try altering coefficients or constants and see how the nature of the solutions changes. It’s a fantastic way to solidify your comprehension and embrace the wonders of algebra!