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$$\bf{-3x-6 > 4x+8}$$

Subtract 4x on both sides.

$$\bf{-3x-6-4x > 8}$$

Combine -3x and -4x to get -7x.

$$\bf{-7x-6 > 8 }$$

$$\bf{-7x > 8+6 }$$

Add 8 and 6 to get 14.

$$\bf{-7x > 14 }$$

Divide both sides by -7. Since -7 is < 0, the inequality direction is changed.

$$\bf{x < \dfrac{14}{-7} }$$

Divide 14 by -7 to get -2.

$$\bf{x < -2 \ \ \to \ \ \ Answer}$$

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Let's solve this inequality by following these steps:

- Add 6 to both sides.
- Subtract 4x from both sides.
- Solve for x.

Step 1: Add 6 to both sides: $$\pmb{-3x-6+6 > 4x+8+6}$$.

Upon simplifying this, we obtain $$\pmb{-3x > 4x+14}$$.

Step 2. Subtract 4x from both sides: $$\pmb{-3x-4x > 4x-4x+14}$$.

Upon simplifying, we obtain $$\pmb{-7x > 14}$$.

Step 3. Divide both sides by -7.

Upon carrying this out, we obtain $$\pmb{x < -2}$$.

$$\ddot\bigstar$$ Remember this...

$$\fbox{\sf{The\:sign\:of\:the\:inequality\:changes\:if\:both\:sides\:are\:divided/multiplied\:by\:a\:negative\:number}}$$

Hope this helped you out, ask in comments if any queries arise.

Best Regards!

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