6. Which of the following values of \( x \) are part of the solution set for the inequality \( -4(x+6)-2 x<8.2 x+10 \) ? Select THREE answers. \( \begin{array}{ll}\text { A. } 3 & -4 x-24-2 x<8.2 x+10 \\ \text { B. } 0 & -6 x-24<8.2 x+10 \\ \text { C. }-2 & -8.2 \\ \text { D. }-4 & -14.2 x-24<10 \\ \text { E. }-7 & -14.2 x<34\end{array} \)

To solve the inequality \( -4(x+6)-2x < 8.2x + 10 \), we will first simplify the left side and then solve for \( x \). ### Step 1: Simplify the left side Start with the inequality: \[ -4(x + 6) - 2x < 8.2x + 10 \] Distributing \( -4 \): \[ -4x - 24 - 2x < 8.2x + 10 \] Combine like terms on the left side: \[ -6x - 24 < 8.2x + 10 \] ### Step 2: Move all terms involving \( x \) to one side Add \( 6x \) to both sides: \[ -24 < 8.2x + 6x + 10 \] \[ -24 < 14.2x + 10 \] ### Step 3: Isolate \( x \) Subtract \( 10 \) from both sides: \[ -24 - 10 < 14.2x \] \[ -34 < 14.2x \] Now, divide both sides by \( 14.2 \): \[ \frac{-34}{14.2} < x \] Calculating \( \frac{-34}{14.2} \): \[ x > -2.3944 \quad (\text{approximately}) \] ### Step 4: Identify the solution set The solution set is \( x > -2.3944 \). ### Step 5: Check the provided options We need to check which of the provided values are greater than \( -2.3944 \): - **A. \( 3 \)**: \( 3 > -2.3944 \) (Valid) - **B. \( 0 \)**: \( 0 > -2.3944 \) (Valid) - **C. \( -2 \)**: \( -2 > -2.3944 \) (Valid) - **D. \( -4 \)**: \( -4 < -2.3944 \) (Not valid) - **E. \( -7 \)**: \( -7 < -2.3944 \) (Not valid) ### Conclusion The values of \( x \) that are part of the solution set for the inequality are: - **A. \( 3 \)** - **B. \( 0 \)** - **C. \( -2 \)** Thus, the correct answers are **A, B, and C**.