for which equation is the order of steps to first diviide both sides by 6 and then to add 8 to both sides?

Answer 1

The order of steps you've described—first dividing both sides by 6 and then adding 8 to both sides—suggests that you are working with an equation of the form:

\[ 6x - 8 = 0 \]

Here's how the steps would work:

1. Start with the equation:
   \( 6x - 8 = 0 \)

2. Divide both sides by 6:
   \[ \frac{6x - 8}{6} = \frac{0}{6} \]
   Simplifying gives:
   \[ x - \frac{8}{6} = 0 \]
   Or:
   \[ x - \frac{4}{3} = 0 \]

3. Now add 8 to both sides:
   \[ x - \frac{4}{3} + 8 = 0 + 8 \]
   This yields:
   \[ x + 8 - \frac{4}{3} = 8 \]

In the context of solving for variable \( x \), it may not be conventional to first divide by 6 before adding a constant; typically, you would isolate the variable after addressing any constants first, such as by adding 8 before dividing by 6. However, it's mathematically valid to perform operations in that order as long as you maintain balance across the equation.