To solve an absolute value equation, you must consider two cases because the value inside the bars can be either positive or negative. First, isolate the absolute value. Then, set the expression inside equal to both c and -c.
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Pro Tips
If c is negative, there are no real solutions because an absolute value cannot be negative.
If c is zero, there is only one solution: x = -b/a.
Always check your solutions by plugging them back into the original equation.
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Fun Facts
"Absolute value equations often represent tolerance in engineering—e.g., 'the part must be 10cm ± 0.1cm'."
"Graphically, the solution represents where a V-shaped graph intersects a horizontal line."
"The symbol |x| was invented by Karl Weierstrass to handle the 'modulus' of complex numbers."
