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}

Answer 1

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

1. For the equation \( -3x + 7 = 10 \):

   \[ -3x + 7 = 10 \]

   Subtract 7 from both sides:

   \[ -3x = 10 - 7 \] \[ -3x = 3 \]

   Now, divide by -3:

   \[ x = \frac{3}{-3} = -1 \]

2. For the equation \( 3x - 9 = 0 \):

   \[ 3x - 9 = 0 \]

   Add 9 to both sides:

   \[ 3x = 9 \]

   Now, divide by 3:

   \[ x = \frac{9}{3} = 3 \]

Now, we combine the solutions from both equations. The solutions are:

• From the first equation, we found \( x = -1 \).
• From the second equation, we found \( x = 3 \).

Thus, the solution set is:

\[ {-1, 3} \]

So the correct response is:

{−1, 3}