Solve 7(x+4)-2/3(×_6<=2(×_3(×+5)?

To solve this expression, we need to simplify it step by step:

1. Distribute the 7 to both terms inside the parentheses:
7(x+4) = 7x + 28

2. Distribute the -2/3 to both terms inside the parentheses:
-2/3(x-6) = -2/3x + 4

3. Combine the terms:
7x + 28 - 2/3x + 4 <= 2(3(x+5))

4. Simplify the right side of the inequality:
2(3(x+5)) = 6(x+5) = 6x + 30

5. Combine the terms on the left side of the inequality:
7x - 2/3x + 28 + 4 <= 6x + 30

6. Combine like terms:
6 1/3x + 32 <= 6x + 30

7. Subtract 6x from both sides:
6 1/3x - 6x + 32 <= 30

8. Simplify:
-5 2/3x + 32 <= 30

Therefore, the solution to the expression 7(x+4) - 2/3(x-6) <= 2(3(x+5)) is -5 2/3x + 32 <= 30.

Step 1: Simplify both sides of the inequality.

```
7(x - 4) - 2/3(x - 6) <= 2(x - 3)(x + 5)
7x - 28 - 2/3(x - 6) <= 2(x^2 + 2x - 15)
7x - 28 - 2/3x + 4 <= 2x^2 + 4x - 30
```

Step 2: Multiply everything by 3 to clear the fractions.

```
21x - 84 - 2x + 12 <= 6x^2 + 12x - 90
```

Step 3: Rearrange the terms into standard form.

```
6x^2 - 9x + 72 <= 0
```

Step 4: Factor the quadratic expression.

```
(3x - 8)(2x - 9) <= 0
```

Step 5: Find the critical points.

The critical points are the values of x that make the expression equal to zero:

```
x = 8/3 and x = 9/2
```

Step 6: Create a sign chart.

```
| Interval | 3x - 8 | 2x - 9 | (3x - 8)(2x - 9) |
|---|---|---|---|
| x < 8/3 | - | - | + |
| 8/3 < x < 9/2 | + | - | - |
| x > 9/2 | + | + | + |
```

Step 7: Find the solution set.

The inequality is true when the expression is less than or equal to zero. From the sign chart, we see that this occurs when:

```
8/3 <= x <= 9/2
```

Therefore, the solution set is [8/3, 9/2]