Match the inequality on the left with the solution on the right. \( \begin{array}{l}6 x-2+6 x \geq-14 \\ \text { [Choose] } \\ -1-2(4 x+6) \leq-37 \\ \text { [Choose] } \\ \text { [Choose] } \\ \text { [Choose] } \\ 8+2 x / 3 \leq 12\end{array} \)

To match the inequalities with their solutions, we first need to solve each inequality step by step. ### Inequality 1: \( 6x - 2 + 6x \geq -14 \) 1. Combine like terms: \[ 12x - 2 \geq -14 \] 2. Add 2 to both sides: \[ 12x \geq -12 \] 3. Divide by 12: \[ x \geq -1 \] ### Inequality 2: \( -1 - 2(4x + 6) \leq -37 \) 1. Distribute the -2: \[ -1 - 8x - 12 \leq -37 \] 2. Combine like terms: \[ -8x - 13 \leq -37 \] 3. Add 13 to both sides: \[ -8x \leq -24 \] 4. Divide by -8 (remember to flip the inequality): \[ x \geq 3 \] ### Inequality 3: \( \frac{2x}{3} + 8 \leq 12 \) 1. Subtract 8 from both sides: \[ \frac{2x}{3} \leq 4 \] 2. Multiply by 3: \[ 2x \leq 12 \] 3. Divide by 2: \[ x \leq 6 \] ### Summary of Solutions 1. \( 6x - 2 + 6x \geq -14 \) gives \( x \geq -1 \) 2. \( -1 - 2(4x + 6) \leq -37 \) gives \( x \geq 3 \) 3. \( \frac{2x}{3} + 8 \leq 12 \) gives \( x \leq 6 \) ### Matching the Inequalities with Solutions - \( 6x - 2 + 6x \geq -14 \) matches with \( x \geq -1 \) - \( -1 - 2(4x + 6) \leq -37 \) matches with \( x \geq 3 \) - \( \frac{2x}{3} + 8 \leq 12 \) matches with \( x \leq 6 \) Now, we can summarize the matches: 1. \( 6x - 2 + 6x \geq -14 \) → \( x \geq -1 \) 2. \( -1 - 2(4x + 6) \leq -37 \) → \( x \geq 3 \) 3. \( \frac{2x}{3} + 8 \leq 12 \) → \( x \leq 6 \)