Determine the solution set of −3x+7=10 or 3x−9=0

Question

(1 point)
Responses

The solution set is null
The solution set is null

{−1,3}
start set negative 1 comma 3 end set

{−1}
start set negative 1 end set

{3}

Answer 1

To determine the solution set for the equation \(-3x + 7 = 10\) or \(3x - 9 = 0\), we need to solve each equation separately.

1. Solve \(-3x + 7 = 10\): \[ -3x + 7 = 10 \] Subtract 7 from both sides: \[ -3x = 10 - 7 \] \[ -3x = 3 \] Divide by -3: \[ x = -1 \]

2. Solve \(3x - 9 = 0\): \[ 3x - 9 = 0 \] Add 9 to both sides: \[ 3x = 9 \] Divide by 3: \[ x = 3 \]

Now, we combine the solutions from both equations. The solutions are \(x = -1\) and \(x = 3\). Therefore, the solution set is:

\[ {-1, 3} \]

So, the correct response is:

{−1, 3}.