Question

Image to Text

Graph the solution of this inequality:
[
\frac{3}{7}(35x - 14) \leq \frac{21x}{2} + 3
]

-7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7

Drag a point to the number line.

Summary

The image presents an inequality problem: (\frac{3}{7}(35x - 14) \leq \frac{21x}{2} + 3). Below the inequality, there is a number line ranging from -7 to 7. There are also draggable points with arrows indicating possible directions, suggesting that the user can place these points on the number line to graph the solution of the inequality.

Answer 1

CLOSED POINT GOING THIS WAY <---- ON 2 NOT -2 THAnK YOU AI now What is the solution set for the inequality?

(–∞, 2]
(–∞, ]
[2, ∞)
[, ∞)

Answer 2

HOORAY!!


Which represents the solution set to the inequality 5.1(3 + 2.2x) > –14.25 – 6(1.7x + 4)?

x < –2.5
x > 2.5
(–2.5, ∞)
(–∞, 2.5)

Answer 3

To solve the inequality

\[
\frac{3}{7}(35x - 14) \leq \frac{21x}{2} + 3,
\]

we first simplify the left side:

1. Distribute \(\frac{3}{7}\):
\[
\frac{3}{7} \times 35x - \frac{3}{7} \times 14 = 15x - 6.
\]
Thus, the left side simplifies to \(15x - 6\).

2. Rewrite the inequality:
\[
15x - 6 \leq \frac{21x}{2} + 3.
\]

3. Next, we need to eliminate the fraction on the right side. We can multiply the entire inequality by 2 (which does not change the inequality sign as we are multiplying by a positive number):
\[
2(15x - 6) \leq 21x + 6.
\]

This simplifies to:
\[
30x - 12 \leq 21x + 6.
\]

4. Now, we isolate \(x\). Subtract \(21x\) from both sides:
\[
30x - 21x - 12 \leq 6,
\]
which simplifies to:
\[
9x - 12 \leq 6.
\]

5. Then, add 12 to both sides:
\[
9x \leq 18.
\]

6. Finally, divide both sides by 9:
\[
x \leq 2.
\]

So, the solution to the inequality is \(x \leq 2\).

### Graphing the solution

To graph the solution on the number line from -7 to 7:

- Draw a closed circle at \(2\) (indicating that \(2\) is included in the solution).
- Shade the region to the left of \(2\) to indicate all values less than or equal to \(2\).

### Final Step
You can drag a point to the number line at \(2\) and shade to the left to graph the solution \(x \leq 2\).

Answer 4

The solution set for the inequality \(x \leq 2\) is expressed in interval notation as:

\[
(-\infty, 2]
\]

This means that \(x\) can take any value from negative infinity up to and including \(2\).

So the correct choice from your options is:

**(–∞, 2]**

Answer 5

To solve the inequality

\[
5.1(3 + 2.2x) > -14.25 - 6(1.7x + 4),
\]

let's break it down step by step.

1. **Distribute on both sides:**

**Left side:**
\[
5.1 \times 3 + 5.1 \times 2.2x = 15.3 + 11.22x.
\]

**Right side:**
\[
-14.25 - 6(1.7x + 4) = -14.25 - 10.2x - 24 = -14.25 - 10.2x - 24 = -38.25 - 10.2x.
\]

So, rewriting the inequality gives us:
\[
15.3 + 11.22x > -38.25 - 10.2x.
\]

2. **Combine like terms:**

First, add \(10.2x\) to both sides:
\[
15.3 + 11.22x + 10.2x > -38.25.
\]
This simplifies to:
\[
15.3 + 21.42x > -38.25.
\]

3. **Now, isolate the term with \(x\):**

Subtract \(15.3\) from both sides:
\[
21.42x > -38.25 - 15.3.
\]
This evaluates to:
\[
21.42x > -53.55.
\]

4. **Divide both sides by \(21.42\):**
\[
x > \frac{-53.55}{21.42}.
\]
Calculating the right-hand side gives:
\[
x > -2.5.
\]

### Conclusion:
The solution of the inequality is:

\[
x > -2.5.
\]

In interval notation, the solution set is:

\[
(-2.5, \infty).
\]

So, the correct answer choice from your options is:

**(–2.5, ∞)**.