Solve the inequality 4/5≤24

Question

GPT-4o mini · Answer

To solve the inequality $ \frac{4}{5} \leq 24 $, we can analyze both sides of the inequality directly. We see that $ \frac{4}{5} = 0.8 $. So, we can rewrite the inequality as: $$ 0.8 \leq 24 $$ This inequality is clearly true because $ 0.8 $ is indeed less than $ 24 $. Since the left side is less than the right side, the solution to the inequality is: $$ \text{True for all values.} $$ Thus, the inequality $ \frac{4}{5} \leq 24 $ holds for all values. There are no restrictions; it is always satisfied.

Monkey balls · Answer

Solve the inequality 4/5d≤24

GPT-4o mini · Answer

To solve the inequality $$ \frac{4}{5}d \leq 24, $$ we can isolate $d$ by following these steps: 1. **Multiply both sides by $ \frac{5}{4} $** (the reciprocal of $ \frac{4}{5} $). Since $ \frac{5}{4} $ is positive, the inequality sign will remain the same: $$ d \leq 24 \cdot \frac{5}{4}. $$ 2. Next, calculate $ 24 \cdot \frac{5}{4} $: $$ 24 \cdot \frac{5}{4} = \frac{24 \cdot 5}{4} = \frac{120}{4} = 30. $$ 3. Therefore, the solution to the inequality is: $$ d \leq 30. $$ In conclusion, the solution to the inequality $ \frac{4}{5}d \leq 24 $ is $$ d \leq 30. $$

Monkey balls · Answer

use the properties of inequality to find the solution to 5(2k-3)≥-3(4-3k)

GPT-4o mini · Answer

To solve the inequality $$ 5(2k - 3) \geq -3(4 - 3k), $$ follow these steps: 1. **Distribute** both sides: $$ 5 \cdot 2k - 5 \cdot 3 \geq -3 \cdot 4 + 3 \cdot 3k $$ This simplifies to: $$ 10k - 15 \geq -12 + 9k. $$ 2. **Rearrange the inequality** to isolate $k$. First, subtract $9k$ from both sides: $$ 10k - 9k - 15 \geq -12 $$ This simplifies to: $$ k - 15 \geq -12. $$ 3. **Add 15 to both sides**: $$ k \geq -12 + 15 $$ This gives: $$ k \geq 3. $$ Thus, the solution to the inequality $5(2k - 3) \geq -3(4 - 3k)$ is $$ k \geq 3. $$

Monkey balls · Answer

what is the inequality depicted on a number line if it starts at -8 and there is a closed circle on 4

GPT-4o mini · Answer

Based on your description, it seems that the inequality starts at $-8$ and includes the point $4$ with a closed circle. Here's how to interpret this:

Open vs. Closed Circle: A closed circle at $4$ means that $4$ is included in the solution set, indicating that the value can be equal to $4$.
Starting Point of -8: Since the inequality begins at $-8$, this suggests that it either stretches towards positive or negative infinity from $-8$.

To depict this accurately:

If the inequality is something like $x \geq -8$ and includes $4$, the solution set includes all numbers greater than or equal to $-8$, and since $4$ is included in this interval (closed circle), it indicates that $4$ is also part of the solution.

Number Line Representation:

Start at $-8$ and draw a closed circle there (meaning $-8$ is included).
Draw an arrow pointing to the right to indicate that it continues to positive infinity.
Place a closed circle at $4$ indicating that $4$ is also included.

Inequality:

The inequality represented here would be:

\[ x \geq -8 \quad \text{and} \quad x \leq 4 \]

This can be combined into one compound inequality:

\[ -8 \leq x \leq 4 \]

This means that the solution set includes all values of $x$ from $-8$ to $4$, inclusive.

Monkey balls · Answer

what is the inequality in a number line that starts at -8 and has an open circle on -5

GPT-4o mini · Answer

Based on your description, where the inequality starts at $-8$ and has an open circle at $-5$, we can interpret this as follows:

Open Circle: An open circle at $-5$ means that $-5$ is not included in the solution set.
Starting Point of $-8$: Since the inequality starts at $-8$, this suggests that the solutions will include all numbers greater than $-8$ but will stop before reaching $-5$.

Number Line Representation:

Start at $-8$: Draw a closed circle at $-8$ (indicating that it is included).
Open Circle at $-5$: Draw an open circle at $-5$ (indicating that it is not included).
Arrow: Draw an arrow to the right, showing that the numbers go towards positive infinity but do not include $-5$.

Inequality:

The inequality represented is:

\[ -8 \leq x < -5 \]

This means that the solution set includes all values of $x$ starting from $-8$ (inclusive) up to but not including $-5$.