(c) \( |2 x+3|=1 \)

To solve the equation \( |2x + 3| = 1 \), you need to break it into two possible cases. The first case is when \( 2x + 3 = 1 \). Solving this gives \( 2x = -2 \) or \( x = -1 \). The second case is when \( 2x + 3 = -1 \). Solving this gives \( 2x = -4 \) or \( x = -2 \). So, the solutions are \( x = -1 \) and \( x = -2 \). This absolute value equation is a great example of how math mirrors real life! Think of it like a distance from zero – whether you’re 1 foot to the right or 1 foot to the left of a starting point, the distance remains the same. This concept is crucial in fields like physics and engineering, where understanding distance and displacement can change everything about how we design structures or analyze movement.