Which of the following inequalities defines the solution set for the inequality \(16-5 x \leq 8 ?\) A. \(x \geq \frac{8}{5}\) B. \(x \geq \frac{5}{8}\) C. \(x \geq-\frac{8}{5}\) D. \(x \geq-\frac{5}{8}\) E. \(x \leq-\frac{8}{5}\)

Being prepared for the ACT is about far more than memorizing formulas and practicing test questions. It's also about understanding the test format and strategies to efficiently find the correct answers.

For students aiming for success on the ACT math section, mastering algebraic inequalities plays a vital role. This is because the ACT often includes questions that test the ability to solve such inequalities. Practice with these kinds of questions not only sharpens your algebra skills but also enhances your test-taking strategies and timing, all of which are crucial for the ACT.

Algebraic inequalities are mathematical expressions where two values are not equal and are separated by inequality symbols like <, >, ≤, or ≥. Solving inequalities involves finding the value or range of values that satisfy the inequality's condition.

To solve algebraic inequalities, one has to perform similar steps as one would with an equation, such as adding, subtracting, multiplying, or dividing both sides by the same number. It's essential to remember that when multiplying or dividing both sides of an inequality by a negative number, the direction of the inequality must be reversed.

Effective test preparation involves creating a study plan, understanding the material, practicing with real or simulated problems, and reviewing incorrect answers. With subjects like math, it's vital to work through problems step by step and understand the reason behind each step, which ensures a solid grip on mathematical reasoning.

Students should make sure to practice problems of varying difficulty levels and types, such as algebraic inequalities, to become familiar with different problem-solving strategies and improve their ability to approach unfamiliar problems on test day. Revising the basics and doing targeted practice, especially in weaker areas, can greatly enhance overall performance.

Mathematical reasoning refers to the logical thought process used to solve math problems. It involves identifying relationships, making conjectures, and constructing proofs. In the context of the algebraic inequality from the original exercise, it is the ability to process and manipulate the inequality to isolate the variable and understand the rule about reversing the inequality symbol when multiplying or dividing by a negative number.

The reasoning process is nurtured by working through multiple problems and understanding the rationale behind each step, rather than just memorizing procedures. Such skills are not only essential for the ACT and other standardized tests but are invaluable for real-life problem-solving situations.