Based on material learned earlier in the course. The purpose...

Based on material learned earlier in the course. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for the final exam.
Solve: $|4-5 x|-8 \leq 3$

Key Concepts

Linear Inequalities

Linear inequalities are inequalities that involve linear expressions. Once an absolute value inequality is converted into a compound inequality, solving the resulting inequalities generally involves applying standard techniques for solving linear inequalities, such as isolating the variable and performing algebraic operations while keeping in mind the reversal of the inequality sign under multiplication or division by a negative number.

Compound Inequalities

Compound inequalities arise when an absolute value inequality is expressed as two separate inequalities. This concept involves solving for the variable within a range defined by two boundary conditions. Understanding compound inequalities is crucial for correctly capturing all possible solutions that satisfy the original absolute value inequality.

Absolute Value

Absolute value is a fundamental concept in mathematics that represents the distance of a number from zero on the number line. It is always non-negative and is defined for any real number regardless of its sign. This concept is essential when dealing with expressions that require measuring distance or magnitude without concern for direction.

Absolute Value Inequalities

Absolute value inequalities involve expressions within absolute value signs and they set up constraints on the distance of a value from a given point. Solving these inequalities requires understanding the definition of absolute value and involves considering both the positive and negative scenarios of the expression inside the absolute value operator.

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