Question

Determine which of the following is the solution set of 2x>−8 and −5x+7=12 .(1 point)
Responses:

{x|x>−1}

{−4}

{x|x>−4}

{−1}

Answer 1

Determine the solution set of −3x+7=10 or 3x−9=0 .(1 point)
Responses


The solution set is null.

{−1,3}

{3}

{−1}

Answer 2

Let's solve the inequalities and equations step by step.

1. **Solving the inequality \(2x > -8\)**:
\[
2x > -8
\]
Divide both sides by 2:
\[
x > -4
\]
So, the solution for this inequality is:
\[
\{x | x > -4\}
\]

2. **Solving the equation \(-5x + 7 = 12\)**:
\[
-5x + 7 = 12
\]
Subtract 7 from both sides:
\[
-5x = 5
\]
Divide both sides by -5 (and remember to reverse the inequality):
\[
x = -1
\]

Now we combine our solutions:
- The solution for the inequality is \(\{x | x > -4\}\).
- The solution for the equation is \(-1\).

Now, let's compare this to the provided options:

1. \(\{x | x > -1\}\)
2. \(\{-4\}\)
3. \(\{x | x > -4\}\)
4. \(\{-1\}\)

The correct solution set based on the inequality \(2x > -8\) is \(\{x | x > -4\}\).

**Final Answer**: \(\{x | x > -4\}\)

Answer 3

Let's solve the equations step by step.

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

2. **Solving 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:
- From \(-3x + 7 = 10\), we have \(x = -1\).
- From \(3x - 9 = 0\), we have \(x = 3\).

So, the solution set is \(-1\) and \(3\), which can be expressed as \(\{-1, 3\}\).

Now, let's compare this to the provided options:

1. The solution set is null.
2. \(\{-1, 3\}\)
3. \(\{3\}\)
4. \(\{-1\}\)

**Final Answer**: \(\{-1, 3\}\)