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

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)