Question

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

{x|x>−4}
left brace x vertical bar x greater than negative 4 right brace

{−1}
left brace negative 1 right brace

{x|x>−1}
left brace x vertical bar x greater than negative 1 right brace

{−4}

Answer 1

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

{−1,3}
left brace negative 1 comma 3 right brace

{3}

Answer 2

To determine the solution set for the given inequalities and equations, we'll solve them step by step.

1. Solve the inequality \( 2x > -8 \):
\[
2x > -8
\]
Divide both sides by 2:
\[
x > -4
\]

2. Solve the equation \( -5x + 7 = 12 \):
\[
-5x + 7 = 12
\]
Subtract 7 from both sides:
\[
-5x = 5
\]
Divide both sides by -5 (remember to reverse the inequality because we are dividing by a negative):
\[
x = -1
\]

Now we have two parts:
- From the inequality \( 2x > -8 \), we get \( x > -4 \).
- From the equation \( -5x + 7 = 12 \), we get \( x = -1 \).

Next, we identify the solution sets:
1. The inequality yields the set \( \{ x | x > -4 \} \).
2. The equation gives a specific solution, \( \{-1\} \).

The solution to the problem involves both the inequality and the equation, but since we are looking for the solution set of 2x > −8 and also finding where these conditions relate to one another:

The main solutions we have are:
- For \( 2x > −8 \), the set of all \( x \) such that \( x > -4 \).
- The specific point \( x = -1 \) is within this range.

Looking at the options available, the inequalities fit:

Thus, the correct response from the provided choices is:

**{x | x > −4}**

Answer 3

To determine the solution set for the given equations, we will solve them step by step.

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

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

Now we have two solutions from these equations:
- From the first equation, we found \( x = -1 \).
- From the second equation, we found \( x = 3 \).

Since the problem states it's an "or" situation, the solution set will include both values.

Thus, the final solution set is:

**{−1, 3}**

This corresponds to the option:

**{−1, 3}**