Question

1/4x+3>-10

solve the equation


How would you put this on a graph?

Should the point be opened or closed
Open
Closed

Where is the shading?
Left
Right

Answer 1

To solve the inequality \( \frac{1}{4}x + 3 > -10 \), follow these steps:

1. **Subtract 3 from both sides**:
\[
\frac{1}{4}x > -10 - 3
\]
\[
\frac{1}{4}x > -13
\]

2. **Multiply both sides by 4** (since we are multiplying by a positive number, the inequality remains the same):
\[
x > -52
\]

### Graphing the Inequality

1. **Draw a number line**.
2. **Locate the point -52** on the number line.
3. Since the inequality is \( > \) (not \( \geq \)), you will use an **open circle** at -52 to indicate that -52 is not included in the solution set.
4. **Shade to the right** of -52 to indicate all the values greater than -52 satisfy the inequality.

### Summary:
- **Open or closed point**: **Open** (circle at -52)
- **Shading direction**: **Right** (from -52 to positive infinity)

This represents all values of \( x \) that are greater than -52.