Questions: Solve the inequality. - x/4 < 7 A. x < -28 B. x > 28 C. x < 28 D. x > -28

Solution Steps

To solve the inequality \(-\frac{x}{4} < 7\), we need to isolate \(x\). We can do this by multiplying both sides of the inequality by \(-4\) and remembering to reverse the inequality sign because we are multiplying by a negative number.

We need to solve the inequality: \[ -\frac{x}{4} < 7 \] and determine which of the given options (A, B, C, D) is correct.

To isolate \( x \), we first need to eliminate the fraction. We do this by multiplying both sides of the inequality by \(-4\). Remember, when we multiply or divide an inequality by a negative number, we must reverse the inequality sign.

\[ -\frac{x}{4} < 7 \quad \text{(original inequality)} \]

Multiplying both sides by \(-4\):

\[ -4 \left( -\frac{x}{4} \right) > 7 \times (-4) \]

Simplify both sides:

\[ x > -28 \]

We now compare our solution \( x > -28 \) with the given options:

• A. \( x < -28 \)
• B. \( x > 28 \)
• C. \( x < 28 \)
• D. \( x > -28 \)

The correct option is D.

Final Answer