Final answer:
To solve the inequality 2|x + 9| + 1 > 7 algebraically, we isolate the absolute value term and split the inequality into two cases. The solution is x < -12 or x > -6.
Step-by-step explanation:
To solve the inequality 2|x + 9| + 1 > 7 algebraically, we first isolate the absolute value term. We can subtract 1 from both sides of the inequality to get 2|x + 9| > 6. Next, we divide both sides by 2 to obtain |x + 9| > 3. This means that the distance between x and -9 on the number line must be greater than 3.
To solve this, we can split the inequality into two cases: x + 9 > 3 and x + 9 < -3. Solving the first case, we subtract 9 from both sides to get x > -6. For the second case, we subtract 9 from both sides to obtain x < -12.
Therefore, the solution to the inequality is x < -12 or x > -6.
Learn more about Solving algebraic inequalities