Problem 87 - Introductory Algebra for College Students

Question

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?

Step-by-Step Solution

Answer

The student made a mistake by not distributing the 3 across all terms in the bracket. Instead of writing \(15x+7\), the correct version should have been \(15x+21\). Practicing more examples can help the student to avoid repeating this mistake.

Step 1: Identify the Mistake

Identifying the error is the first step. The student multiplied the 3 outside the bracket with the \(5x\) term but missed to do the same with the 7. Therefore, the right-hand side of their equation achieved incorrect formation as \(15x+7\) instead of \(15x+21\).

Step 2: Explain the Correct Method

To correct this error, explain that the number outside the brackets \(3\) in this case should be multiplied with every term inside the brackets. Therefore, the equation should have been written as \(3*(5x+7) = 15x + 21\).

Step 3: Additional Practice

The student should be encouraged to practice this property with more examples and varying complexity to understand and avoid repeating the error. Understanding the basic properties of algebra is important to solve the equations correctly.