Question

1 of 21 of 2 Items
Question 1
1. Which of the following values for b makes the inequality −32.5 − 6b ≥48.5
true?(2 points)
Responses

-12.5
-12.5

-13.5
-13.5

-12
-12

-12
-12
Question 2
2. Which set expresses the solution to the compound inequality −2≤2x+13−4<1
?(2 points)
Responses

{x: 3≤x<7}
{x: 3≤x<7}

{x: 52≤x<7}
{x: 52≤x<7}

{x: −32≤x<1}
{x: −32≤x<1}

{x: 52≤x<1}
{x: 52≤x<1}
Question 3
3. Which option is the solution to the inequality −12g+18>−5g+53
?(2 points)
Responses

g<−5
g<−5

g<71−17
g<71−17

g>71−17
g is greater than 71 over negative 17

g>−5

Answer 1

Let's solve each question step by step.

### Question 1: Solve the inequality \(-32.5 - 6b \geq 48.5\)

1. Start with the given inequality:
\[-32.5 - 6b \geq 48.5\]

2. Add \(32.5\) to both sides:
\[-6b \geq 48.5 + 32.5\]
\[-6b \geq 81\]

3. Divide both sides by \(-6\) (remember to reverse the inequality sign):
\[b \leq -\frac{81}{6}\]
\[b \leq -13.5\]

The correct value for \(b\) that makes the inequality true is **-13.5**.

### Question 2: Solve the compound inequality \(-2 \leq 2x + 13 - 4 < 1\)

1. Simplify the middle expression:
\[-2 \leq 2x + 9 < 1\]

2. Break it into two parts:
- \(-2 \leq 2x + 9\)
- \(2x + 9 < 1\)

3. Solve the first part:
\[-2 - 9 \leq 2x\]
\[-11 \leq 2x\]
\[-\frac{11}{2} \leq x\]
\[x \geq -5.5\]

4. Solve the second part:
\[2x < 1 - 9\]
\[2x < -8\]
\[x < -4\]

Combining these inequalities, we get:
\[ -5.5 \leq x < -4 \]
This does not match any of the provided responses directly.

Based on the outcome, none of your provided choices seem correct.

### Question 3: Solve the inequality \(-12g + 18 > -5g + 53\)

1. Rearrange the inequality:
\[-12g + 5g > 53 - 18\]
\[-7g > 35\]

2. Divide by \(-7\) and flip the inequality:
\[g < -5\]

So the correct option for this inequality is **g < −5**.

### Summary of Answers:
1. **-13.5**
2. The solution does not match any option provided.
3. **g < −5**