Solve the inequality 45d≤24

Question

.(1 point)
The solution to the inequality is d≤
.

Answer 1

To solve the inequality \( 45d \leq 24 \), we need to isolate \( d \). We do this by dividing both sides of the inequality by 45:

\[ d \leq \frac{24}{45} \]

Now, simplify \( \frac{24}{45} \):

\[ \frac{24}{45} = \frac{8}{15} \]

Thus, the solution to the inequality is:

\[ d \leq \frac{8}{15} \]

So, the final answer is:

d ≤ \(\frac{8}{15}\).

Answer 2

Use 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 3

To solve the inequality \( 5(2k - 3) \geq -3(4 - 3k) \), we start by expanding both sides.

First, expand the left side:

\[ 5(2k - 3) = 10k - 15 \]

Now, expand the right side:

\[ -3(4 - 3k) = -12 + 9k \]

Now, substitute these expansions back into the inequality:

\[ 10k - 15 \geq -12 + 9k \]

Next, we will isolate \( k \). First, subtract \( 9k \) from both sides:

\[ 10k - 9k - 15 \geq -12 \]

This simplifies to:

\[ k - 15 \geq -12 \]

Now, add 15 to both sides:

\[ k \geq 3 \]

Thus, the solution to the inequality is:

k ≥ 3.

Answer 4

Use the image to answer the question.

A number line ranges from negative 8 to 8 in increments of 1. A closed point is plotted at 4. An arrow extends indefinitely left from the closed point past negative 8 along the number line.

What inequality is depicted in the graph?

(1 point)

Answer 5

The description you provided indicates that there is a closed point plotted at \(4\) on the number line, and there is an arrow extending indefinitely to the left from this point. A closed point means that \(4\) is included in the solution set.

Since the arrow extends indefinitely to the left from \(4\), this means that the values are less than or equal to \(4\).

Therefore, the inequality depicted in the graph is:

\[ x \leq 4 \]

This indicates that all numbers less than or equal to \(4\) are included in the solution set.