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Jessica is asked to solve the equation 1x+1=xx+1+2x+1. She multiplies both sides of the equation by x + 1 and determines that x must be – 1. Why is Jessica’s answer incorrect?

a. She made a calculation error.
b. The equation is unsolvable.
c. She didn't distribute the (x + 1) correctly.
d. She didn't simplify the equation.

User Sleepyhead
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1 Answer

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Final answer:

Jessica's solution of x = -1 for the equation might be incorrect if she made a mistake in calculation, improperly distributed the multiplier (x + 1), or failed to simplify correctly. Multiplication should be applied correctly to prevent errors in solving equations.

Step-by-step explanation:

Jessica is asked to solve the equation 1/(x+1) = x/(xx+1) + 2/(x+1). The question is pointing out an error in the process of solving this equation. Jessica multiplies both sides by the same term, x + 1, to eliminate the denominators. It's possible that Jessica's answer of x = -1 is incorrect because she either made a calculation error, didn't distribute (x + 1) correctly, or didn't simplify the equation correctly. Multiplying by x + 1 should indeed apply to every term on either side, as per the rules of multiplication, and this needs to be done carefully to avoid any mistakes.

In this scenario, the error could be any of the provided options, except for the equation being unsolvable, as equations of this type generally have a solution unless there's a contradiction. For example, if the equation after proper simplification and distribution lead to a statement such as 0 = 1, only then could we classify the equation as unsolvable.

It is critical that each step in solving the equation is carried out with precision, from distribution to simplification, to avoid arriving at an incorrect solution.

User OddNorg
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