Question

1. use the properties of equality to identify the error made in the constructed argument.

• circle or underline the error.
• justify your answer by explaining how you would correct the mistake.

given: ( 3x + 1 = - 14 ) prove: ( x = - 5 )
proof: we know ( 3x + 1 = - 14 ) because it is given. by the subtraction property, we can obtain ( 3x = - 15 ). lastly, ( x = - 5 ) by the multiplication property.

Explanation:

Step1: Analyze the last step

The last step claims to use the Multiplication Property. But to solve \(3x=-15\) for \(x\), we should use the Division Property of Equality.
The Division Property of Equality states that if \(a = b\) and \(c
eq0\), then \(\frac{a}{c}=\frac{b}{c}\).
In the equation \(3x=-15\), to isolate \(x\), we divide both sides of the equation by \(3\).

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Answer:

The error is in the statement “by the Multiplication Property” in the last step. To correct it, we should use the Division Property of Equality. We divide both sides of the equation \(3x=-15\) by \(3\) (since \(3
eq0\)) to get \(x = - 5\).