Which inequality is true when the value of nn is minus, 15−15?

Question

Answer
Multiple Choice Answers
n, minus, 4, is greater than, minus, 10n−4>−10
minus, n, minus, 4, is less than, 10−n−4<10
minus, n, minus, 4, is less than, minus, 10−n−4<−10
minus, n, minus, 4, is greater than, 10−n−4>10

Answer 1

To evaluate the inequalities given the condition \( n = -15 \), we will substitute \( n \) into each inequality and see which one holds true.

1. First Inequality: \[ -n - 4 > -10 \] Substituting \( n = -15 \): \[ -(-15) - 4 > -10 \implies 15 - 4 > -10 \implies 11 > -10 \quad \text{(True)} \]

2. Second Inequality: \[ -n - 4 < 10 \] Substituting \( n = -15 \): \[ -(-15) - 4 < 10 \implies 15 - 4 < 10 \implies 11 < 10 \quad \text{(False)} \]

3. Third Inequality: \[ -n - 4 < -10 \] Substituting \( n = -15 \): \[ -(-15) - 4 < -10 \implies 15 - 4 < -10 \implies 11 < -10 \quad \text{(False)} \]

4. Fourth Inequality: \[ -n - 4 > 10 \] Substituting \( n = -15 \): \[ -(-15) - 4 > 10 \implies 15 - 4 > 10 \implies 11 > 10 \quad \text{(True)} \]

So, we have:

• The first inequality is true.
• The second inequality is false.
• The third inequality is false.
• The fourth inequality is true.

Thus, both the first and the fourth inequalities are true when \( n = -15 \). However, since we are only to select one option, the first inequality: \[ -n - 4 > -10 \] is a valid answer.

The answer from the multiple choices that is true is:

• \( -n - 4 > -10 \)

Answer 2

Solve the inequality and graph the solution on the line provided.
9, plus, 4, x, is greater than or equal to, 37
9+4x≥
37
Answer
Attempt 1 out of 2


Inequality Notation:
Number Line:

Answer 3

To solve the inequality \( 9 + 4x \geq 37 \), we will isolate \( x \).

Steps to solve:

1. Subtract 9 from both sides: \[ 4x \geq 37 - 9 \] \[ 4x \geq 28 \]

2. Divide by 4: \[ x \geq \frac{28}{4} \] \[ x \geq 7 \]

Solution in inequality notation:

The solution to the inequality is: \[ x \geq 7 \]

Graphing the solution on a number line:

• Draw a number line.
• Place a closed circle (or dot) at \( 7 \) since the inequality includes the equal to sign (≥).
• Shade the line to the right of \( 7 \) to indicate that the solution includes all numbers greater than or equal to \( 7 \).

Summary:

• Inequality Notation: \( x \geq 7 \)
• Number Line:
  • Use a closed circle at \( 7 \) and shade to the right.

If you need a visual representation, imagine the following:

<---|---|---|---|---|---|---|---|---|---|---|---
    4   5   6 (7)========================>

The closed circle at 7 indicates that \( 7 \) is included in the solution set. The arrow extending to the right indicates all values greater than \( 7 \) are included.

Answer 4

Solve the inequality and graph the solution on the line provided.
8, plus, 3, x, is greater than, 23
8+3x>
23
Answer
Attempt 1 out of 2


Inequality Notation:
Number Line:
Click and drag to plot line.

Answer 5

To solve the inequality \( 8 + 3x > 23 \), let’s follow the steps to isolate \( x \).

Steps to Solve the Inequality:

1. Subtract 8 from both sides: \[ 3x > 23 - 8 \] \[ 3x > 15 \]

2. Divide by 3: \[ x > \frac{15}{3} \] \[ x > 5 \]

Solution in Inequality Notation:

The solution to the inequality is: \[ x > 5 \]

Graphing the Solution on a Number Line:

1. Draw a number line.
2. Place an open circle at \( 5 \) because the inequality does not include \( 5 \) (it is strictly greater).
3. Shade the line to the right of \( 5 \) to indicate that all numbers greater than \( 5 \) are included in the solution.

Summary:

• Inequality Notation: \( x > 5 \)
• Number Line:
  • Use an open circle at \( 5 \) and shade to the right.

If you need to visualize it:

<---|---|---|---|---|---|---|---|---|---|---|---
    2   3   4 (5)========================>

This representation shows an open circle at \( 5 \) with shading extending to the right, indicating that all values greater than \( 5 \) are part of the solution.

Feel free to click and drag to plot the line as needed!

Answer 6

Solve the inequality and graph the solution on the line provided.
5, x, plus, 54, is greater than or equal to, 74
5x+54≥
74
Answer
Attempt 1 out of 2


Inequality Notation:
Number Line:

Answer 7

To solve the inequality \( 5x + 54 \geq 74 \), let's follow the steps to isolate \( x \).

Steps to Solve the Inequality:

1. Subtract 54 from both sides: \[ 5x \geq 74 - 54 \] \[ 5x \geq 20 \]

2. Divide by 5: \[ x \geq \frac{20}{5} \] \[ x \geq 4 \]

Solution in Inequality Notation:

The solution to the inequality is: \[ x \geq 4 \]

Graphing the Solution on a Number Line:

1. Draw a number line.
2. Place a closed circle at \( 4 \) because the inequality includes \( 4 \) (it is "greater than or equal to").
3. Shade the line to the right of \( 4 \) to indicate that all numbers greater than or equal to \( 4 \) are included in the solution.

Summary:

• Inequality Notation: \( x \geq 4 \)
• Number Line:
  • Use a closed circle at \( 4 \) and shade to the right.

If you were to visualize this:

<---|---|---|---|---|---|---|---|---|---|---|---
    1   2   3 (4)========================>

This representation shows a closed circle at \( 4 \) with shading extending to the right, indicating that all values \( 4 \) and greater are part of the solution.

You can now drag and plot this on your provided number line!