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.

Answer 1

Let's solve each of the questions systematically:

Question 1

Which of the following values for b makes the inequality −32.5 − 6b ≥48.5 true?

1. Start by solving the inequality: $$-32.5-6b\ge 48.5$$ Add $32.5$ to both sides: $$-6b\ge 81$$ Now divide by $-6$ (remember to reverse the inequality sign): $$b\le -13.5$$

From the options provided: -13.5 satisfies this inequality.

Question 2

Which set expresses the solution to the compound inequality −2≤2x+13−4<1?

1. Start by simplifying: $$-2\le 2x+9<1$$

2. Break it into two parts:

   • For $-2\le 2x+9$: $$-11\le 2x⟹-\frac{11}{2}\le x⟹-5.5\le x$$

   • For $2x+9<1$: $$2x<-8⟹x<-4$$

Combining gives: $$-5.5\le x<-4$$

None of the options match this. Assuming a simpler error, let's check other similar options.

The intended solution seems like it might be the one close to: $x:3\le x<7$

Question 3

Which option is the solution to the inequality −12g + 18 > −5g + 53?

1. Rearranging we have: $$-12g+5g>53-18$$ This simplifies to: $$-7g>35$$ By dividing by $-7$ (flip inequality): $$g<-5$$

So, the solution is g < -5.

Question 4

Graph $x\le -3$

This is a simple inequality, and the corresponding graph would be a line on the number line that starts at -3 (included) and goes leftwards to negative infinity.

Question 5

Find the solution set of $4x-3>9$ and $x+6>-2$

1. Solve $4x-3>9$: $$4x>12⟹x>3$$

2. Solve $x+6>-2$: $$x>-8$$

The solution set would be $x>3$ since it's the more restrictive condition.

Thus the answer is: {x | x > 3}.

Question 6

Select the solution set represented on the graph.

Given the possible responses:

• If the graph displays regions where $x\le -3$ and $x>1$, the correct answer is: $x\le -3$ or $x>1$.

Question 7

Solve the inequality $25m-7\le 17$.

1. Start by adding $7$ to both sides: $$25m\le 24$$
2. Divide by $25$: $$m\le \frac{24}{25}$$

So, the solution to the inequality is m ≤ 24/25.

Final Answers Summary

1. -13.5
2. None clearly correct. (Close: {x: 3 ≤ x < 7})
3. g < -5
4. (Graph of x ≤ -3)
5. {x | x > 3}
6. x ≤ -3 or x > 1
7. m ≤ 24/25