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

Question

?(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 go through these questions one by one.

Question 2

Solve the compound inequality: \[ -2 \leq 2x + 13 - 4 < 1 \] Simplifying the middle expression: \[ -2 \leq 2x + 9 < 1 \]

Now break it into two parts:

1. \(-2 \leq 2x + 9\): \[ -2 - 9 \leq 2x \implies -11 \leq 2x \implies -\frac{11}{2} \leq x \implies x \geq -5.5 \]

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

Putting these together, we find: \[-5.5 \leq x < -4\]

The correct response is not available in the options provided.

Question 3

Solve the inequality: \[ -12g + 18 > -5g + 53 \] Rearranging gives: \[ -12g + 5g > 53 - 18 \implies -7g > 35 \] Dividing by -7 (remember to switch the inequality sign): \[ g < -5 \]

Response: \(g < -5\)

Question 4

Graph \( x \leq -3 \)

On the graph, the line will be solid (since it includes equality) at \(x = -3\) and shaded to the left, showing all values less than or equal to -3.

Question 5

Find the solution set of:

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

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

The combined solution set is \(x > 3\).

Response: \({x | x > 3}\)

Question 6

Select the solution set represented on the graph.

For a graph showing \(x \leq -3\) or \(x > 1\):

• The correct option would be \(x \leq -3\) or \(x > 1\).

Question 7

Solve the inequality: \[ 25m - 7 \leq 17 \] Adding 7 to both sides: \[ 25m \leq 24 \] Dividing by 25: \[ m \leq \frac{24}{25} \]

Response: The solution to the inequality is \(m \leq \frac{24}{25}\).

If you need any clarifications or further assistance, feel free to ask!