Solve the inequality and graph the solution on the line provided $$ 2 x+16

Question

Solve the inequality and graph the solution on the line provided $$ 2 x+16<2 $$

UpStudy AI · Accepted Answer

To solve the inequality $$ 2x + 16 < 2 $$ and graph its solution on a number line, follow these steps:

### **Step 1: Solve the Inequality**

1. **Subtract 16 from both sides** to isolate the term with $$ x $$:
   $$
   2x + 16 - 16 < 2 - 16
   $$
   $$
   2x < -14
   $$

2. **Divide both sides by 2** to solve for $$ x $$:
   $$
   \frac{2x}{2} < \frac{-14}{2}
   $$
   $$
   x < -7
   $$

### **Solution**

The solution to the inequality is:
$$
x < -7
$$
This means all real numbers **less than -7** satisfy the inequality.

### **Graphing the Solution on a Number Line**

Here's how to represent the solution graphically:

```
<====o---------------------------------------------->
        -7
```

**Explanation of the Graph:**

- **Number Line:** The horizontal line represents all real numbers.
- **Open Circle at -7 ("o"):** 
  - An open circle is used at $$ x = -7 $$ to indicate that -7 is **not included** in the solution (since the inequality is strictly less than).
- **Arrow to the Left (<====):**
  - The arrow pointing to the left from -7 shows that all numbers **less than -7** are part of the solution.

### **Summary**

- **Algebraic Solution:** $$ x < -7 $$
- **Graphical Representation:** An open circle at -7 with shading extending to the left, indicating all values less than -7 are solutions.
The solution to the inequality $$ 2x + 16 < 2 $$ is $$ x < -7 $$. On the number line, this is represented by an open circle at -7 with an arrow pointing to the left, indicating all numbers less than -7 are solutions.

Solve the inequality and graph the solution on the line provided \[ 2 x+16<2 \]

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