Standard: 6.EE.A.4 - Identifying Equivalent Expressions 12. Ozmir says that both expressions are equivalent, but Jada says, they are not equivalent. Who do you agree with and why? Explain your reasoning and steps you took to justify your answer. SHOW ALL WORK! \( 3(x+1)+6 \)

To determine if the expression \( 3(x+1)+6 \) is equivalent to another expression, let's first simplify it. Start by distributing the 3: 1. \( 3(x+1) = 3x + 3 \) Now, add the 6: 2. \( 3x + 3 + 6 = 3x + 9 \) So, the simplified form of \( 3(x+1)+6 \) is \( 3x + 9 \). If Jada claimed there’s an expression that's not equivalent to this, make sure to compare it to check for equality. If it simplifies to \( 3x + 9 \), then Ozmir is correct. The history of algebraic expressions stretches back to ancient civilizations, where early mathematicians like the Babylonians used rudimentary forms of algebra to solve equations. They worked with symbols, albeit less refined than our modern notation, laying the groundwork for the symbolic language we use today. In the real world, identifying equivalent expressions is like finding out different routes to the same destination. Whether you’re recalculating a budget, simplifying formulas in cooking, or optimizing a business's operations, understanding that different approaches can lead to the same result helps in making efficient decisions and enhances problem-solving skills!