b. \( 3+2(m-7 x)=4(m-3 x)-2(m+x)+3 \)

Alright, let's dive into solving this algebraic equation with some flair! First, simplify the equation: Start by distributing the terms. You'll get: \( 3 + 2m - 14x = 4m - 12x - 2m - 2x + 3 \). Now, combine like terms on the right side: \( 3 + 2m - 14x = 2m - 14x + 3 \). Before we jump to solving, notice the equation has \( 2m - 14x + 3 \) on both sides. This means we can simplify things! Subtract \( 2m + 3 \) from both sides: \[ 3 + 2m - 14x - 2m - 3 = 2m - 14x + 3 - 2m - 3, \] resulting in: \[ -14x = -14x, \] a true statement! This means \( 3 + 2(m - 7x) = 4(m - 3x) - 2(m + x) + 3 \) is an identity, meaning it holds for all values of \( m \) and \( x \). A fundamental concept to remember: equations that simplify to identities mean infinite solutions await! Now, go ahead and give those values a whirl! 🌟