Solve. \[ -50<7 a+6<-8 \] A \( 28 \) D \( \quad-8

Ask by Burton Stanley. in the United States

Jan 23,2025

To solve the compound inequality \(-50 < 7a + 6 < -8\), we can break it down into two parts. 1. Solve the left inequality: \(-50 < 7a + 6\) Subtract 6 from both sides: \(-50 - 6 < 7a\) \(-56 < 7a\) Divide by 7: \(-8 < a\) or \(a > -8\) 2. Solve the right inequality: \(7a + 6 < -8\) Subtract 6 from both sides: \(7a < -8 - 6\) \(7a < -14\) Divide by 7: \(a < -2\) Combining the results, we have: \(-8 < a < -2\) Thus, the solution is: \(-8 < a < -2\) This corresponds to option D: \(-8 < a < -2\).