Question

Which of the following values for b makes the
inequality -32.5 - 6b ≥ 48.5 true?
(1 point)

-13

-13.5

-12.5

-12

Answer 1

Which of the following equations has the solution set {-3} ? (1 point)
48+8= -4
4x + 8 = 4
• 4х — 8 = 4
• 4х — 8 = —4

Answer 2

Which of the following equations has the solution set {-3} ? (1 point)
4x+8= -4
4x + 8 = 4
4х — 8 = 4
4х — 8 = —4

Answer 3

To solve the inequality \(-32.5 - 6b \geq 48.5\), we start by isolating the term with \(b\).

1. Add 32.5 to both sides:

\[
-6b \geq 48.5 + 32.5
\]

\[
-6b \geq 81
\]

2. Now, divide both sides by -6. Remember that when you divide or multiply an inequality by a negative number, the direction of the inequality changes:

\[
b \leq \frac{81}{-6}
\]

Simplifying \(\frac{81}{-6}\):

\[
b \leq -13.5
\]

Now we need to check which of the given values makes this inequality true:

- **-13**: This is not less than or equal to -13.5 (False)
- **-13.5**: This is equal to -13.5 (True)
- **-12.5**: This is greater than -13.5 (False)
- **-12**: This is greater than -13.5 (False)

The value that makes the inequality true is:

**-13.5**

Answer 4

To determine which equation has the solution set \(\{-3\}\), we can substitute \(-3\) into each equation and see if it satisfies the equation.

1. **Equation: \(48 + 8 = -4\)**
- This is a false statement (56 = -4).

2. **Equation: \(4x + 8 = 4\)**
- Substitute \(x = -3\):
\[
4(-3) + 8 = 4
\]
\[
-12 + 8 = 4
\]
\[
-4 \neq 4 \quad \text{(False)}
\]

3. **Equation: \(4x - 8 = 4\)**
- Substitute \(x = -3\):
\[
4(-3) - 8 = 4
\]
\[
-12 - 8 = 4
\]
\[
-20 \neq 4 \quad \text{(False)}
\]

4. **Equation: \(4x - 8 = -4\)**
- Substitute \(x = -3\):
\[
4(-3) - 8 = -4
\]
\[
-12 - 8 = -4
\]
\[
-20 \neq -4 \quad \text{(False)}
\]

None of the provided equations correctly evaluates to true when \(x = -3\). Therefore, based on this analysis, none of the equations have the solution set \(\{-3\}\).

However, let's carefully analyze one more time and solve directly for \(x\) in the equations (the last two):

3. **Equation: \(4x - 8 = 4\)**
- Adding 8 to both sides:
\[
4x = 12
\]
- Dividing by 4:
\[
x = 3 \quad \text{(not -3)}
\]

4. **Equation: \(4x - 8 = -4\)**
- Adding 8 to both sides:
\[
4x = 4
\]
- Dividing by 4:
\[
x = 1 \quad \text{(not -3)}
\]

All calculations confirm that none of the provided equations yield a solution set of \(\{-3\}\). Please double-check the equations given.

Answer 5

Let's check each of the equations to find which one has \(-3\) as the solution by substituting \(-3\) for \(x\).

1. **Equation: \(4x + 8 = -4\)**
- Substitute \(x = -3\):
\[
4(-3) + 8 = -4
\]
\[
-12 + 8 = -4
\]
\[
-4 = -4 \quad \text{(True)}
\]

2. **Equation: \(4x + 8 = 4\)**
- Substitute \(x = -3\):
\[
4(-3) + 8 = 4
\]
\[
-12 + 8 = 4
\]
\[
-4 \neq 4 \quad \text{(False)}
\]

3. **Equation: \(4x - 8 = 4\)**
- Substitute \(x = -3\):
\[
4(-3) - 8 = 4
\]
\[
-12 - 8 = 4
\]
\[
-20 \neq 4 \quad \text{(False)}
\]

4. **Equation: \(4x - 8 = -4\)**
- Substitute \(x = -3\):
\[
4(-3) - 8 = -4
\]
\[
-12 - 8 = -4
\]
\[
-20 \neq -4 \quad \text{(False)}
\]

The only equation that has the solution set \(\{-3\}\) is:

**\(4x + 8 = -4\)**.