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

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 \(a(b - c)=ab - ac\). So, \(-4\times3=-12\) and \(-4\times(-5x) = 20x\).

Step2: Write the Resulting Inequality

After distributing, the left - hand side of the inequality becomes \(-12 + 20x\), and the inequality sign remains \(\geq\) (because we are only distributing a negative number and not multiplying or dividing the entire inequality by a negative number yet). So the inequality after the first step is \(-12 + 20x\geq -6x + 9\).

Answer:

-12 + 20x ≥ -6x + 9 (the last option)