(1) \( 7 x-4(-x-14)=122 \)

To solve \( 7x - 4(-x - 14) = 122 \), start by distributing the -4 to both terms inside the parentheses: \( -4(-x) = 4x \) and \( -4(-14) = 56 \). This changes the equation to \( 7x + 4x + 56 = 122 \). Combine like terms: \( 11x + 56 = 122 \). Now, isolate the variable by subtracting 56 from both sides: \( 11x = 66 \). Finally, divide both sides by 11 to find \( x = 6 \). Who knew solving equations could be a bit like piecing together a puzzle? Much like how you discover hidden shapes in a jigsaw, each step simplifies the equation until the solution reveals itself! When you're dealing with equations, always keep an eye out for those sneaky negative signs and distributive properties. They can easily flip the whole equation on its head if overlooked. So, double-check each step as you go along!