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Question

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