Question

800 + 6x = 10x + 1000 (after subtracting 6x from both sides: 800 = 4x + 1000; after subtracting 1000 from both sides: -200 = 4x; after dividing both sides by 4: -50 = x)

Explanation:

Step1: Start with the equation

We have the equation \( 800 + 6x=110x + 1000 \) (assuming a typo, maybe \(10x\) instead of \(110x\)? But following the given steps). First, subtract \(6x\) from both sides:
\( 800 + 6x-6x=110x + 1000-6x \)
Simplifies to \( 800 = 104x+ 1000 \)? Wait, but in the given work, it's \(4x\), so maybe the original equation was \(800 + 6x = 10x+1000\). Let's follow the given steps. The first step in the work is subtracting \(6x\) from both sides:
\( 800+6x - 6x=110x + 1000-6x \) (but in the work, it becomes \(800 = 4x + 1000\), so maybe the original right - hand side was \(10x\), so \(10x-6x = 4x\)). So with the corrected (based on the work) original equation \(800 + 6x=10x + 1000\). After subtracting \(6x\) from both sides:
\( 800=4x + 1000 \)

Step2: Subtract 1000 from both sides

\( 800-1000=4x + 1000-1000 \)
\( - 200 = 4x \)

Step3: Divide both sides by 4

\( \frac{-200}{4}=\frac{4x}{4} \)
\( x=- 50 \)

Answer:

\(x = - 50\)