Respuesta :
Hi student, let me help you out!
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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: [tex]\pmb{-3x-6+6 > 4x+8+6}[/tex].
Upon simplifying this, we obtain [tex]\pmb{-3x > 4x+14}[/tex].
Step 2. Subtract 4x from both sides: [tex]\pmb{-3x-4x > 4x-4x+14}[/tex].
Upon simplifying, we obtain [tex]\pmb{-7x > 14}[/tex].
Step 3. Divide both sides by -7.
Upon carrying this out, we obtain [tex]\pmb{x < -2}[/tex].
[tex]\ddot\bigstar[/tex] Remember this...
[tex]\fbox{\sf{The\:sign\:of\:the\:inequality\:changes\:if\:both\:sides\:are\:divided/multiplied\:by\:a\:negative\:number}}[/tex]
Hope this helped you out, ask in comments if any queries arise.
Best Regards!
[tex]\star\bigstar\overline{\overline{\underline{\underline{\bold{Reach\:far.\:Aim\:high.\:Dream\:big.}}}}}\bigstar\star[/tex]
[tex]\underline{\rule{300}{5}}[/tex]
[tex]\bf{-3x-6 > 4x+8}[/tex]
Subtract 4x on both sides.
[tex]\bf{-3x-6-4x > 8}[/tex]
Combine -3x and -4x to get -7x.
[tex]\bf{-7x-6 > 8 }[/tex]
Add 6 to both sides.
[tex]\bf{-7x > 8+6 }[/tex]
Add 8 and 6 to get 14.
[tex]\bf{-7x > 14 }[/tex]
Divide both sides by -7. Since -7 is < 0, the inequality direction is changed.
[tex]\bf{x < \dfrac{14}{-7} }[/tex]
Divide 14 by -7 to get -2.
[tex]\bf{x < -2 \ \ \to \ \ \ Answer}[/tex]
[tex]\red{\boxed{\green{\boxed{\boldsymbol{\purple{Pisces04}}}}}}[/tex]
