Question

1. $-3x - 7 = -8x - 57$ (with some handwritten additions like +57 on both sides, resulting in $-3x + 50$ and $-8x$)

Explanation:

Step1: Start with the equation \(-3x - 7 = -8x - 57\)

We want to solve for \(x\), so we can add \(8x\) to both sides to get rid of the \(-8x\) on the right.
\(-3x + 8x - 7 = -8x + 8x - 57\)
\(5x - 7 = -57\)

Step2: Add 7 to both sides

To isolate the term with \(x\), we add 7 to both sides.
\(5x - 7 + 7 = -57 + 7\)
\(5x = -50\)

Step3: Divide both sides by 5

To solve for \(x\), we divide both sides by 5.
\(\frac{5x}{5} = \frac{-50}{5}\)
\(x = -10\)

Wait, but looking at the handwritten work, maybe there was a typo or a different approach. Let's re - examine the handwritten equations. If we consider the first line as \(-3x - 7=-8x - 57\) (ignoring the handwritten additions for a moment as they seem to be a work - in - progress):

Step1: Add \(8x\) to both sides

\(-3x+8x - 7=-8x + 8x-57\)
\(5x-7=-57\)

Step2: Add 7 to both sides

\(5x-7 + 7=-57 + 7\)
\(5x=-50\)

Step3: Divide by 5

\(x = \frac{-50}{5}=-10\)

If we consider the handwritten additions (like \(+57\) on both sides), let's try that:

Step1: Start with \(-3x - 7=-8x - 57\), add 57 to both sides

\(-3x-7 + 57=-8x-57 + 57\)
\(-3x + 50=-8x\)

Step2: Add \(8x\) to both sides

\(-3x+8x + 50=-8x + 8x\)
\(5x+50 = 0\)

Step3: Subtract 50 from both sides

\(5x+50-50=0 - 50\)
\(5x=-50\)

Step4: Divide by 5

\(x=\frac{-50}{5}=-10\)

Answer:

\(x = - 10\)