To solve the inequality \(\frac{x}{-3} - 2 < -4\), follow these steps:
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Isolate the term with \(x\): Start by adding 2 to both sides of the inequality. \[ \frac{x}{-3} < -4 + 2 \] \[ \frac{x}{-3} < -2 \]
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Multiply both sides by -3: Remember that when you multiply or divide both sides of an inequality by a negative number, you must flip the inequality sign. \[ x > -2 \times -3 \] \[ x > 6 \]
Therefore, the solution to the inequality is: \[ x > 6 \]