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

Question

(1 point)
Responses

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

The solution set is null
The solution set is null

{−1}
start set negative 1 end set

{3}
start set 3 end set

Answer 1

To find the solution set of the equations \( -3x + 7 = 10 \) or \( 3x - 9 = 0 \), we will solve each equation separately.

Solving the first equation:

\[ -3x + 7 = 10 \] Subtract 7 from both sides: \[ -3x = 10 - 7 \] \[ -3x = 3 \] Now divide by -3: \[ x = -1 \]

Solving the second equation:

\[ 3x - 9 = 0 \] Add 9 to both sides: \[ 3x = 9 \] Now divide by 3: \[ x = 3 \]

Solution Set

The solution set is the union of the solutions from both equations. Therefore, the solutions are: \[ {-1, 3} \]

Thus, the correct response is: \({-1, 3}\)