Here are the essential concepts you must grasp in order to answer the question correctly.
Absolute Value
Absolute value represents the distance of a number from zero on the number line, regardless of direction. For any real number 'a', the absolute value is denoted as |a| and is defined as |a| = a if a ≥ 0, and |a| = -a if a < 0. Understanding absolute value is crucial for solving equations that involve it, as it leads to two possible cases based on the sign of the expression inside the absolute value.
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Linear Equations
A linear equation is an equation of the first degree, meaning it involves only linear terms and can be expressed in the form ax + b = c, where a, b, and c are constants. Solving linear equations involves isolating the variable on one side of the equation. In the context of the given problem, once the absolute value is resolved, the resulting equations will be linear and can be solved using standard algebraic techniques.
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Inequalities
Inequalities express a relationship where one side is not necessarily equal to the other, using symbols such as <, >, ≤, or ≥. When solving inequalities, the solution set may include a range of values rather than a single number. In the context of the given question, understanding how to manipulate and solve inequalities is essential, especially when considering the implications of absolute values, which can lead to multiple cases to analyze.
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