\begin{tabular}{l|l}$$ \square $$ & Question 3 \ $$ 2-3 x-12 $$ \ $$ \bigcirc x3 $$ \ $$ O x

Question

\begin{tabular}{l|l}$$ \square $$ & Question 3 \ $$ 2-3 x<5 x-22 $$ \ $$ \bigcirc x>-12 $$ \ $$ \bigcirc x<3 $$ \ $$ O x>3 $$ \ $$ O x<12 $$\end{tabular}

UpStudy AI · Accepted Answer

Let's solve the inequality step by step: $$ 2 - 3x < 5x - 22 $$ 1. **Move all terms involving $$x$$ to one side and constant terms to the other side:** $$ 2 - 3x - 5x < -22 $$ $$ 2 - 8x < -22 $$ 2. **Subtract 2 from both sides to isolate the term with $$x$$:** $$ -8x < -24 $$ 3. **Divide both sides by $$-8$$.** **_Important:_** When you divide or multiply both sides of an inequality by a negative number, you must **reverse the inequality sign**. $$ x > 3 $$ **Solution:** $$ x > 3 $$ --- **Based on the provided options:** - $$ \bigcirc $$ $$ x > -12 $$ - $$ \bigcirc $$ $$ x < 3 $$ - $$ \bigcirc $$ $$ x > 3 $$ - $$ \bigcirc $$ $$ x < 12 $$ **The correct answer is:** $$ x > 3 $$ The solution to the inequality $$2 - 3x < 5x - 22$$ is $$x > 3$$.

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