1/4x+3>-10

Question

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.