1. Which of the following values for b makes the inequality −32.5 − 6b ≥48.5

Question

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
g is greater than negative 5
Question 4
4. Graph x≤−3
.(2 points)
Responses

Question 5
5. Find the solution set of 4x−3>9
and x+6>−2
.(2 points)
Responses

The solution set is null
The solution set is null

{x | x>3}
{x | x>3}

{3, −8}
{3, −8}

{x | x>−8}
{x | x>−8}
Question 6
6. Select the solution set represented on the graph.

(2 points)
Responses

x≤−3 or x>1
x≤−3 or x>1

x≤−3 or x≥1
x≤−3 or x≥1

x<−3 or x>1
x<−3 or x>1

x<−3 and x>1
x<−3 and x>1
Question 7
7. Solve the inequality 25m−7≤17
.(2 points)
The solution to the inequality is
Make sure your variable is on the left.
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Answer 1

Let's solve each question one by one.

Question 1

Inequality: \( -32.5 - 6b \geq 48.5 \)

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

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

Thus, the correct value for \(b\) is -13.5.

Question 2

Compound Inequality: \( -2 \leq 2x + 13 - 4 < 1 \)

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

2. Split into two inequalities: \[ -2 \leq 2x + 9 \quad \text{and} \quad 2x + 9 < 1 \]

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

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

5. Combine the results: \[ -5.5 \leq x < -4 \]

The closest set from the options reflecting this inequality is {x: -5.5 ≤ x < -4}, however, it seems it isn't listed. The correct option should be checked according to the available responses.

Question 3

Inequality: \( -12g + 18 > -5g + 53 \)

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

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

The solution is g < -5.

Question 4

Graph: \( x \leq -3 \)

To graph this inequality, you would draw a number line, place a closed dot (since -3 is included) on -3, and shade to the left to indicate all values less than or equal to -3.

Question 5

1. Solve \( 4x - 3 > 9 \): \[ 4x > 12 \implies x > 3 \]

2. Solve \( x + 6 > -2 \): \[ x > -8 \]

The solution set is the intersection of the two results, which is \( x > 3 \).

Thus, the response should be {x | x > 3}.

Question 6

Based on the given options and graphs, if the graph indicates values where \(x \leq -3\) or \(x > 1\), then the appropriate choice would be \(x \leq -3\) or \(x > 1\).

Question 7

Inequality: \( 25m - 7 \leq 17 \)

1. Add \(7\) to both sides: \[ 25m \leq 24 \]

2. Divide by \(25\): \[ m \leq \frac{24}{25} \]

So the solution to the inequality is \( m \leq \frac{24}{25} \), which can be expressed as \( m \leq 0.96 \).

If you need any more clarification or specific formatting for responses, let me know!