Question

what is a correct first step in solving the inequality $-4(3 - 5x) \geq -6x + 9$?
\boxed{-12 - 20x \leq -6x + 9} \boxed{-12 + 20x \leq -6x + 9} \boxed{-12 - 20x \geq -6x + 9}
\boxed{-12 + 20x \geq -6x + 9}

Explanation:

Step1: Apply Distributive Property

To solve the inequality \(-4(3 - 5x) \geq -6x + 9\), the first step is to distribute the \(-4\) across the terms inside the parentheses. The distributive property states that \(a(b + c)=ab+ac\). Here, \(a = - 4\), \(b = 3\) and \(c=-5x\). So, \(-4\times3+(-4)\times(-5x)\). Calculating each term: \(-4\times3=-12\) and \((-4)\times(-5x) = 20x\). So the left - hand side becomes \(-12 + 20x\) and the inequality remains \(-12 + 20x\geq-6x + 9\) (since we are just simplifying the left - hand side using the distributive property and not changing the inequality sign yet as we are not multiplying or dividing by a negative number).

Answer:

\(-12 + 20x\geq-6x + 9\) (the last option in the given set of options)