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Chapter 6: Problem 80

An algebra student incorrectly used the distributive property and wrote \(3(5 x+7)=15 x+7\). If you were that student's teacher, what would you say to help the student avoid this kind of error?

Short Answer

Expert verified
The student should be instructed that in the distributive property, \(a (b + c) = ab + ac\), 'a' must be distributed to both 'b' and 'c'. In the student's equation, the 3 should multiply both 5x and 7, resulting in \(15x + 21\), not \(15x + 7\).

Step by step solution

01

Identify the student's error

The student has written \(3 (5x + 7) = 15x + 7\). This shows a misunderstanding of the distributive property because the multiplication by 3 wasn't applied to the 7 within the parentheses.
02

Apply the correct distributive property

The correct way to use the distributive property on \(3 (5x + 7)\) is to multiply each term inside the bracket by 3. This yields \(3 * 5x + 3 * 7 = 15x + 21\).
03

Compare the corrected equation to student's equation

Upon comparing the two equations, \(3 (5x + 7) = 15x + 7\) and \(3 (5x + 7) = 15x + 21\), it's clear that the student didn't correctly apply the distributive property to the term 7.

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