1.1.1 \( (2 x-1)(x+5)=0 \)

To solve the equation \( (2x-1)(x+5)=0 \), you can use the zero-product property, which states that if the product of two factors is zero, at least one of them must be zero. So, set each factor to zero: 1. \( 2x - 1 = 0 \) leads to \( 2x = 1 \) and \( x = \frac{1}{2} \). 2. \( x + 5 = 0 \) gives \( x = -5 \). Therefore, the solutions to the equation are \( x = \frac{1}{2} \) and \( x = -5 \). Now, here’s a fun fact: both of these solutions come from solving linear equations, showcasing how simple algebraic expressions can yield multiple solutions! Also, remember that these are a great way to practice isolating variables, which is a fundamental skill in algebra.