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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
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.

1 answer

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: \[ -32.5 - 6b \geq 48.5 \] Add \(32.5\) to both sides: \[ -6b \geq 81 \] Now divide by \(-6\) (remember to reverse the inequality sign): \[ b \leq -13.5 \]

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

  2. Break it into two parts:

    • For \(-2 \leq 2x + 9\): \[ -11 \leq 2x \implies -\frac{11}{2} \leq x \implies -5.5 \leq x \]

    • For \(2x + 9 < 1\): \[ 2x < -8 \implies x < -4 \]

Combining gives: \[ -5.5 \leq x < -4 \]

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: \({ x : 3 \leq x < 7 }\)

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 \(x \leq -3\)

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

  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 \(x \leq -3\) and \(x > 1\), the correct answer is: \(x \leq -3\) or \(x > 1\).

Question 7

Solve the inequality \(25m - 7 \leq 17\).

  1. Start by adding \(7\) to both sides: \[ 25m \leq 24 \]
  2. Divide by \(25\): \[ m \leq \frac{24}{25} \]

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