Algebral $$ \begin{array}{l} ext { hich values of } x ext { would be part of the solution set for } 3 x+10

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Algebral $$ \begin{array}{l}	ext { hich values of } x 	ext { would be part of the solution set for } 3 x+10<2(5 x-2) \ 0-10 \ 02 \ 0 \ 0\end{array} $$

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To determine which values of $$ x $$ satisfy the inequality: $$ 3x + 10 < 2(5x - 2) $$ Let's solve the inequality step by step. ### Step 1: Expand the Right Side First, distribute the 2 on the right side: $$ 3x + 10 < 10x - 4 $$ ### Step 2: Bring Like Terms Together Subtract $$ 3x $$ from both sides to gather the $$ x $$-terms on one side: $$ 10 < 7x - 4 $$ Next, add 4 to both sides to isolate the term with $$ x $$: $$ 14 < 7x $$ ### Step 3: Solve for $$ x $$ Divide both sides by 7 to solve for $$ x $$: $$ 2 < x $$ Or equivalently: $$ x > 2 $$ ### Conclusion The solution set consists of all real numbers greater than 2. **Therefore, any value of $$ x $$ where $$ x > 2 $$ is part of the solution set.** If we consider the options provided: - **-10**: Not greater than 2. ❌ - **0-10**: Includes values greater than 2 (specifically from 2 to 10). ✅ - **02**: Assuming this is a typo and meant to be 2, it's the boundary value. ❌ (since $$ x $$ must be greater than 2, not equal to 2) - **0**: Not greater than 2. ❌ **Correct Option:** $$ 0-10 $$ (assuming it represents values between 2 and 10) Any value of $$ x $$ greater than 2 is part of the solution set.

Algebral \( \begin{array}{l}\text { hich values of } x \text { would be part of the solution set for } 3 x+10<2(5 x-2) \\ 0-10 \\ 02 \\ 0 \\ 0\end{array} \)

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