Question

1. error analysis describe and correct the error in the first step of solving the equation.

\\(\frac{7x + 1}{2x + 5}+ 4 = \frac{10x - 3}{3x}\\)
\\((2x + 5)3x\cdot\frac{7x + 1}{2x + 5}+ 4 = \frac{10x - 3}{3x}\cdot(2x + 5)3x\\)

Explanation:

Step1: Identify the error

When eliminating the denominators, every term on both sides of the equation must be multiplied by the least common denominator (LCD), which is \((2x + 5)3x\). In the given first step, the term \(4\) was not multiplied by \((2x + 5)3x\).

Step2: Correct the first step

Multiply each term by \((2x + 5)3x\) to get:
\[
(2x + 5)3x\cdot\frac{7x + 1}{2x + 5}+(2x + 5)3x\cdot4=\frac{10x - 3}{3x}\cdot(2x + 5)3x
\]

Answer:

The error is that the term \(4\) was not multiplied by the least common denominator \((2x + 5)3x\). The correct first step is \((2x + 5)3x\cdot\frac{7x + 1}{2x + 5}+(2x + 5)3x\cdot4=\frac{10x - 3}{3x}\cdot(2x + 5)3x\).