What Is Wrong? One step in the following list contains an...

What Is Wrong? One step in the following list contains an error. Identify it and explain what is wrong.
$$
\begin{aligned}
x &=2 \\
3 x-2 x &=2 \\
3 x &=2 x+2 \\
x^{2}+3 x &=x^{2}+2 x+2 \\
x^{2}+3 x-10 &=x^{2}+2 x-8 \\
(x-2)(x+5) &=(x-2)(x+4) \\
x+5 &=x+4 \\
1 &=0
\end{aligned}
$$

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Key Concepts

Domain Restrictions and Division by Zero

This concept is integral in algebra to ensure that any variable manipulation does not violate the rules of the operations being performed. Specifically, when canceling terms from both sides of an equation, care must be taken to exclude values that would make the canceled expression zero, in order to avoid division by zero and the subsequent logical errors in the solution.

Cancellation of Common Factors

When an equation includes a common factor on both sides, it may be tempting to cancel it; however, it is important to verify that the factor is not zero, as division by zero is undefined. Canceling without checking can lead to the loss of potential solutions or the introduction of errors in the manipulation of the equation.

Algebraic Manipulation

This concept involves performing operations such as addition, subtraction, multiplication, division, and factoring on both sides of an equation while maintaining equality. It is crucial in algebra to carefully apply these operations, ensuring that any steps taken are reversible and do not omit potential solutions or introduce extraneous ones.

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