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 and inequalities that involve expressions within absolute value symbols.
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Inequalities
Inequalities express a relationship between two expressions that are not necessarily equal. They use symbols such as <, >, ≤, and ≥ to indicate whether one side is less than, greater than, or equal to the other. Solving inequalities often involves similar steps to solving equations, but requires careful consideration of the direction of the inequality when multiplying or dividing by negative numbers.
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Solving Equations
Solving equations involves finding the value(s) of the variable that make the equation true. This process often includes isolating the variable on one side of the equation through various algebraic manipulations, such as adding, subtracting, multiplying, or dividing both sides. In the context of absolute value equations, it may require considering multiple cases based on the definition of absolute value.
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