To solve the equation \(-15x = 24 + 16x = 3x - 24\) and transform it into the form \(x = a\), where \(a\) is a number, let's first clarify the equation. It appears to be a compound equation, so we should treat it as two separate equations:
- \(-15x = 24 + 16x\)
- \(-15x = 3x - 24\)
Let's focus on the first equation \(-15x = 24 + 16x\).
From this equation, we can apply the following transformations:
- B: Subtract \(16x\) from both sides: \[ -15x - 16x = 24 \implies -31x = 24. \] Then, simplifying gives: \[ x = -\frac{24}{31}. \]
Next, let’s look at the second equation \(-15x = 3x - 24\).
- D: Add \(15x\) to both sides: \[ 0 = 18x - 24 \implies 18x = 24, \] then simplifying gives: \[ x = \frac{24}{18} = \frac{4}{3}. \]
Both approaches indicate that we can manipulate the equation toward a single solution for \(x\).
The correct options that apply are:
- B: Subtract 15x from both sides of the equation and then simplify (to isolate \(x\)).
- D: Add 3x to both sides of the equation and then simplify (to also isolate \(x\)).
In summary, the two steps that can be taken to simplify into the form \(x = a\) are B and D.