$$ \frac{4}{3} x+11 \geq 7 $$ or $$ -4 x-3 \leq-23 $$ Solution Interval Notation $$ \square $$

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UpStudy AI · Accepted Answer

To solve the compound inequality:

$$
\frac{4}{3}x + 11 \geq 7 \quad \text{or} \quad -4x - 3 \leq -23
$$

we'll solve each inequality separately and then combine the solutions using interval notation.

### 1. Solving $$\frac{4}{3}x + 11 \geq 7$$:

$$
\frac{4}{3}x + 11 \geq 7
$$

Subtract 11 from both sides:

$$
\frac{4}{3}x \geq 7 - 11
$$

$$
\frac{4}{3}x \geq -4
$$

Multiply both sides by $$\frac{3}{4}$$ to solve for $$x$$:

$$
x \geq -4 \times \frac{3}{4}
$$

$$
x \geq -3
$$

### 2. Solving $$-4x - 3 \leq -23$$:

$$
-4x - 3 \leq -23
$$

Add 3 to both sides:

$$
-4x \leq -23 + 3
$$

$$
-4x \leq -20
$$

Divide both sides by $$-4$$ (remember to reverse the inequality sign when dividing by a negative number):

$$
x \geq 5
$$

### Combining the Solutions:

The solutions to the individual inequalities are:
- $$x \geq -3$$
- $$x \geq 5$$

Since the original compound inequality uses "or," we take the union of these solutions. The interval $$x \geq -3$$ already includes $$x \geq 5$$, so the combined solution is:

$$
x \geq -3
$$

### Interval Notation:

$$
[-3, \infty)
$$

**Answer:** $$[-3, \infty)$$
The solution is $$ x \geq -3 $$, which in interval notation is $$[-3, \infty)$$.

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