Not reversing the sign when dividing by negative

❌ The Mistake in Action

Solve $-3x < 12$

Wrong: $x < -4$

🧠 Why It Happens

Students divide by $-3$ correctly but forget to reverse the inequality sign. They treat it exactly like an equation.

✅ The Fix

When you multiply or divide by a negative number, you must reverse the inequality sign.

$-3x < 12$

Divide by $-3$ AND flip the sign: $$x > -4$$

Why? If $-3x < 12$, think about $x = -5$: $-3(-5) = 15$, and $15 < 12$ is FALSE. But $x = -3$: $-3(-3) = 9$, and $9 < 12$ is TRUE. So $x$ must be greater than $-4$, not less than.

🔍 Spot the Mistake

Can you identify where this student went wrong?

Solve $-3x < 12$

Divide by $-3$: $x < -4$

Click on the line that contains the error.

📚 Related Topics

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