Here are the essential concepts you must grasp in order to answer the question correctly.
Absolute Value
Absolute value measures the distance of a number from zero on the number line, regardless of direction. For any real number x, the absolute value is defined as |x| = x if x ≥ 0 and |x| = -x if x < 0. In the context of equations, this means that |A| = B implies A = B or A = -B, which is crucial for solving equations involving absolute values.
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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 given problem, the absolute value equation leads to two separate linear equations that need to be solved.
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Isolating the Variable
Isolating the variable is a fundamental technique in algebra used to solve equations. This involves manipulating the equation through addition, subtraction, multiplication, or division to get the variable alone on one side. In the context of the given absolute value equation, after breaking it into two cases, isolating x will help find the solutions for the original equation.
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