Question

Multiple Equations or Inequalities Quick Check
2 of 52 of 5 Items
Question
Determine the solution set of −3x+7=10
or 3x−9=0
.(1 point)
Responses

The solution set is null.
The solution set is null.

{−1}
left brace negative 1 right brace

{3}
left brace 3 right brace

{−1,3}

Answer 1

To solve the equations \(-3x + 7 = 10\) and \(3x - 9 = 0\), we'll solve each equation individually.

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

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

Now we combine the solutions from both equations. The solutions are \(x = -1\) and \(x = 3\).

Thus, the solution set is:
\[
\{-1, 3\}
\]

So, the correct response is:
\(\{−1, 3\}\).