Question

which of the following best models the solution set of the given inequality?
-3(x - 3) > -6

Explanation:

Step1: Expand the left - hand side

Use the distributive property \(a(b - c)=ab - ac\). Here \(a=-3\), \(b = x\), \(c = 3\).
\(-3(x - 3)=-3x+9\). So the inequality becomes \(-3x + 9>-6\).

Step2: Subtract 9 from both sides

\(-3x+9-9>-6 - 9\).
\(-3x>-15\).

Step3: Divide both sides by - 3 and reverse the inequality sign

When dividing an inequality by a negative number, the direction of the inequality sign changes.
\(\frac{-3x}{-3}<\frac{-15}{-3}\).
\(x < 5\).

Answer:

The first option (the number line with an open circle at \(5\) and the arrow pointing to the left) is the correct model for the solution set \(x < 5\).