Which of the following values for b makes the

Question

inequality -32.5 - 6b ≥ 48.5 true?
(1 point)

-13

-13.5

-12.5

-12

Answer 1

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 2

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 3

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 4

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 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:

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