Solve the equation. If your answer is a decimal, round to one decimal place. \( { }^{* * *} \) If there is more than one solution, separate them with a comma - no parentheses. If there is no solution, type: DNE \( 7|8 x+6|+9=30 \) Submit Question

To solve the equation \(7|8x + 6| + 9 = 30\), first, isolate the absolute value term: 1. Subtract 9 from both sides: \(7|8x + 6| = 21\) 2. Divide both sides by 7: \(|8x + 6| = 3\) Now, we can set up two cases for the absolute value: **Case 1:** \(8x + 6 = 3\) Subtracting 6 from both sides gives: \(8x = -3\) Dividing by 8 yields: \(x = -\frac{3}{8} \approx -0.4\) **Case 2:** \(8x + 6 = -3\) Subtracting 6 from both sides gives: \(8x = -9\) Dividing by 8 yields: \(x = -\frac{9}{8} = -1.125\) Thus, there are two solutions: -0.4, -1.1.