Final answer:
To determine Andrew's mistake in solving the inequality, we must compare his steps with the correct arithmetic procedures. Without specific steps, it is difficult to pinpoint the error, but he should distribute properly, change inequality signs when dividing by negatives, and perform identical operations on both sides.
Step-by-step explanation:
Andrew needs to solve the inequality carefully following the arithmetic rule of equality, meaning whatever operation is performed on one side must be applied to the other side. However, to identify Andrew's mistake, we need to check his steps against the standard procedure for solving inequalities. Applying the distributive property correctly, simplifying each side, and then isolating the variable x will yield the correct solution to the inequality. So, let's break down each step:
- Firstly, distribute the -4 across the terms inside the parenthesis: -4(X + 8) = -4X - 32.
- Add 25 to both sides if necessary.
- Simplify each side before combining like terms.
- Remember to change the direction of the inequality sign when multiplying or dividing by a negative number.
- Do not add or subtract terms unless you perform the same operation to both sides, and ensure all like terms are correctly combined.
Without the original steps Andrew took, it's challenging to identify his mistake. However, following the rules mentioned should help Andrew and others avoid common errors like the ones listed in the options (such as not changing the inequality sign when dividing by a negative or incorrectly adding terms).