Question

Determine the solution set of 2x > - 8 and - 5x + 7 = 12
{-1}
{-4}
{ x| x > -1}
{ x| x > -4}

Answer 1

Determine the solution set of -3x + 7 = 10 or 3x - 9 = 0.
{-1}
{3}
{-1,3}
The solution set is null.

Answer 2

To solve the inequalities and the equation given in the problem, we'll analyze each one step by step.

1. **Solving the inequality \(2x > -8\)**:

To isolate \(x\), divide both sides of the inequality by 2:
\[
x > -4
\]

2. **Solving the equation \(-5x + 7 = 12\)**:

First, subtract 7 from both sides:
\[
-5x = 12 - 7
\]
\[
-5x = 5
\]

Next, divide both sides by -5 (remember to reverse the inequality sign when dividing by a negative number):
\[
x = -1
\]

3. **Determining the solution set**:

The solution to the inequality \(x > -4\) gives us all numbers greater than -4, while the solution to the equation gives us a specific value \(x = -1\).

The solution set will depend on where these solutions overlap or what they suggest:
- The inequality \(x > -4\) indicates that any number greater than -4 is valid.
- The specific solution from the equation is \(x = -1\), which is valid since -1 is indeed greater than -4.

Given these analyses, we can select the correct representation of the solution sets:
- \( \{ x | x > -4 \} \) includes all numbers greater than -4, whereas \( \{ x | x > -1 \} \) would only include numbers greater than -1, which does not incorporate the entire range given by the inequality.

Thus, the solution set of the inequality and the equation is expressed as:
\[
\{ x | x > -4 \}
\]

So the correct answer is \(\{ x | x > -4 \}\).

Answer 3

Let's solve the two equations provided in the problem one by one.

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

2. **Solving the equation \(3x - 9 = 0\)**:
\[
3x - 9 = 0
\]
Add 9 to both sides:
\[
3x = 9
\]
Now, divide by 3:
\[
x = 3
\]

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

Since the solution is given in terms of "or," we combine both solutions:

The complete solution set is:
\[
\{-1, 3\}
\]

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