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Equations are the foundation of mathematics, and solving them involves finding the values that make them true. Linear equations [], of the form ax + b = 0, are solved by isolating the variable. Quadratic equations [], with an x² term (ax² + bx + c = 0), can often be solved by factoring or by using the quadratic formula []. Special attention is required for equations involving radicals [], where squaring both sides can introduce extraneous solutions that must be checked. Polynomials [], with higher powers of x, can become complex to solve but may be factorable. Inequalities [] function similarly to equations but use comparison signs, and solving them involves isolating the variable and testing intervals defined by zeros for polynomial inequalities [].
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Equations are the foundation of mathematics, and solving them involves finding the values that make them true. Linear equations [], of the form ax + b = 0, are solved by isolating the variable. Quadratic equations [], with an x² term (ax² + bx + c = 0), can often be solved by factoring or by using the quadratic formula []. Special attention is required for equations involving radicals [], where squaring both sides can introduce extraneous solutions that must be checked. Polynomials [], with higher powers of x, can become complex to solve but may be factorable. Inequalities [] function similarly to equations but use comparison signs, and solving them involves isolating the variable and testing intervals defined by zeros for polynomial inequalities [].