The solution to a math problem is the correct answer for the problem. The solution to an equation is a set of one or more values that, when substituted for a variable, make an equation or system true or consistent. To solve a math problem is to find the solution of the problem.
For example, given the equation x + 3 = 5, the solution is x = 2. x = 2 satisfies the equation x + 3 = 5. Try substituting 2 for x in the equation. The equation becomes 2 + 3 = 5. Since this is a true statement, we know that 2 is a solution to the equation.
An extraneous solution is a apparent solution that does not satisfy the equation or system. Extraneous solutions can occur when multiplying both sides of an equation by a variable, and by squaring both sides of an equation:
|1||This is the equation to solve.|
|2||Square both sides of the equation. This is the step where and extraneous solution is introduced. Expand both sides of the equation by applying the exponents.|
|3||Subtract x from both sides of the equation.|
|4||Factor the left hand side of the equation.|
|5||The factors imply solutions of 4 and 1.|
|6||Check the solution x=4 by substituting 4 for x in the original equation. The equation now simplifies to 2=2. Since this is a true statement that satisfies the equation, 2 is a solution to the equation. 2 is not an extraneous solution to the equation.|
|7||Check the solution x=1 by substituting 1 for x in the original equation. The equation now simplifies to -1=1. Since this is a false statement that does not satisfy the equation, 1 is a not solution to the equation. 1 is an extraneous solution.|
|Table 1: Finding an extraneous solution.|
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