Question

Solve the inequality 4/5d≤24
.(1 point)
The solution to the inequality is d≤ ( )

Answer 1

se the properties of inequality to find the solution to 5(2k−3)≥−3(4−3k)
.(1 point)
The solution to the inequality is k≥( )

Answer 2

use the graph to answer the question

-12, -11, -10, -9, -8, -7, -6, -5, -4, -3, -2, -1, 0

there's a hollow circle on top of -9 dragging an arrow to zero
What inequality is depicted in the graph?
x( )

Answer 3

To solve the inequality \( \frac{4}{5}d \leq 24 \), we can follow these steps:

1. **Multiply both sides by 5** to eliminate the fraction:
\[
5 \cdot \frac{4}{5}d \leq 5 \cdot 24
\]
This simplifies to:
\[
4d \leq 120
\]

2. **Divide both sides by 4** to isolate \( d \):
\[
\frac{4d}{4} \leq \frac{120}{4}
\]
This simplifies to:
\[
d \leq 30
\]

So, the solution to the inequality is:
\[
d \leq 30
\]

Thus, the answer is \( d \leq (30) \).

Answer 4

To solve the inequality \( 5(2k - 3) \geq -3(4 - 3k) \), we can follow these steps:

1. **Distribute** on both sides:
\[
10k - 15 \geq -12 + 9k
\]

2. **Rearrange the equation** to move all terms involving \( k \) to one side and constant terms to the other side. Subtract \( 9k \) from both sides:
\[
10k - 9k - 15 \geq -12
\]
This simplifies to:
\[
k - 15 \geq -12
\]

3. **Add 15** to both sides to isolate \( k \):
\[
k \geq -12 + 15
\]
This simplifies to:
\[
k \geq 3
\]

So, the solution to the inequality is:
\[
k \geq 3
\]

Thus, the final answer is \( k \geq (3) \).

Answer 5

The hollow circle at \(-9\) indicates that \(-9\) is not included in the solution, and the arrow extending to \(0\) suggests that \(x\) can take any value between \(-9\) and \(0\), not including \(-9\) but including values up to \(0\).

This can be represented with the inequality:

\[
x < 0 \quad \text{and} \quad x > -9
\]

Combining these gives the compound inequality:

\[
-9 < x < 0
\]

This is usually written in interval notation as:

\[
x \in (-9, 0)
\]

So, the inequality depicted in the graph is:

\[
x \in (-9, 0)
\]