To solve the inequality \( \frac{1}{4}x + 3 > -10 \), follow these steps:
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Subtract 3 from both sides: \[ \frac{1}{4}x > -10 - 3 \] \[ \frac{1}{4}x > -13 \]
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Multiply both sides by 4 (since we are multiplying by a positive number, the inequality remains the same): \[ x > -52 \]
Graphing the Inequality
- Draw a number line.
- Locate the point -52 on the number line.
- 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.
- 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.