Question

1. find the error. consider the equation: \\(-3(5 - 4x) = 57\\) a student solves the equation shown below. step 1: \\(-15 - 12x = 57\\) step 2: \\(-12x = 72\\) step 3: \\(x = -6\\) in which step does the first error occur?

Explanation:

Step1: Analyze Step 1

When distributing \(-3\) into \((5 - 4x)\), we use the distributive property \(a(b - c)=ab - ac\). Here, \(a=-3\), \(b = 5\), and \(c = 4x\). So, \(-3\times5=-15\) and \(-3\times(-4x)=12x\). The correct expansion should be \(-15 + 12x = 57\), but the student wrote \(-15 - 12x = 57\), which is an error.

Step2: Check Step 2 (if needed)

Since there's an error in Step 1, we can conclude the first error is in Step 1.

Answer:

The first error occurs in Step 1.