34. A part of Jennifer's work to solve the equation \( 2\left(6 x^{2}-3\right)=11 x^{2}-x \) is shown below. Given: \( 2\left(6 x^{2}-3\right)=11 x^{2}-x \) Step 1: \( 12 x^{2}-6=11 x^{2}-x \) Which property justifies her first step? A. identity property of multiplication B. multiplication property of equality C. commutative property of multiplication D. distributive property of multiplication over subtraction

Jennifer's first step involves distributing the 2 across the terms inside the parentheses. This means she's applying the principle that you can multiply a sum or difference by a number. The correct answer is D, the distributive property of multiplication over subtraction, which allows you to express \( 2\left(6 x^{2}-3\right) \) as \( 12 x^{2} - 6 \). If you think about it, the distributive property is like a superhero for equations—helping you break down complicated expressions and making them easier to solve! Remember, mastering this property is a key step in leveling up your algebra skills!