Question

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

Explanation:

Step1: Apply Distributive Property

The distributive property states that \(a(b + c)=ab + ac\). For \(-4(3 - 5x)\), we multiply \(-4\) with each term inside the parentheses: \(-4\times3+(-4)\times(-5x)\).
Calculating each part: \(-4\times3=-12\) and \((-4)\times(-5x) = 20x\). So, \(-4(3 - 5x)=-12 + 20x\).
The original inequality is \(-4(3 - 5x)\geq-6x + 9\), after applying the distributive property, we get \(-12 + 20x\geq-6x + 9\).

Answer:

D. \(-12 + 20x \geq -6x + 9\) (assuming the last option is D, if the options are labeled as A, B, C, D with the last one being \(-12 + 20x \geq -6x + 9\))