\( \overline { 4 } + 6 > 15 \)

To solve the inequality \( \overline{4} + 6 > 15 \), we first need to clarify what \( \overline{4} \) means. In mathematical notation, \( \overline{4} \) typically represents a repeating decimal, specifically \( 4.4444\ldots \). Let's denote \( x = \overline{4} = 4.4444\ldots \). Now, we can rewrite the inequality: \[ x + 6 > 15 \] Next, we will isolate \( x \) by subtracting 6 from both sides: \[ x > 15 - 6 \] Calculating the right side gives: \[ x > 9 \] Now, substituting back \( x = \overline{4} \): \[ \overline{4} > 9 \] Since \( \overline{4} \) (which is approximately 4.4444) is not greater than 9, the inequality does not hold true. Thus, the final conclusion is: \[ \overline{4} + 6 > 15 \text{ is false.} \]