Question

reasoning solve the inequality. use pencil and paper. describe how you know the direction of the inequality sign without solving the inequality.
-4x > 12
what are the solutions? select the correct choice below and fill in the answer box to complete your choice.
a. x >
b. x ≥
c. x ≤
d. x <

Explanation:

Step1: Recall inequality rule

When dividing/multiplying an inequality by a negative number, the inequality sign flips. Here, we have \(-4x > 12\). We need to solve for \(x\) by dividing both sides by \(-4\).

Step2: Apply the rule

Divide both sides of \(-4x > 12\) by \(-4\). Since we divide by a negative number (\(-4\)), the inequality sign (\(>\)) flips to \(<\). So, \(\frac{-4x}{-4} < \frac{12}{-4}\), which simplifies to \(x < -3\). Also, to know the direction without solving, we note that the coefficient of \(x\) is negative. When solving for \(x\) (dividing by a negative), the inequality sign will reverse. So the solution should have a \(<\) sign, matching option D with the value \(-3\).

Answer:

D. \(x < -3\)