Solve for \( x \). \( 2 x+4 \frac{1}{5}=9 \)
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To solve for \( x \), first convert \( 4 \frac{1}{5} \) into an improper fraction. This is equal to \( 4 \times 5 + 1 = 20 + 1 = 21 \), so \( 4 \frac{1}{5} \) is \( \frac{21}{5} \). Now rewrite the equation: \[ 2x + \frac{21}{5} = 9 \] Next, subtract \( \frac{21}{5} \) from both sides: \[ 2x = 9 - \frac{21}{5} \] To perform this subtraction, convert \( 9 \) to a fraction with a common denominator of \( 5 \): \[ 9 = \frac{45}{5} \] Now, subtract: \[ 2x = \frac{45}{5} - \frac{21}{5} = \frac{45 - 21}{5} = \frac{24}{5} \] Now divide both sides by \( 2 \): \[ x = \frac{24}{5} \div 2 = \frac{24}{5} \times \frac{1}{2} = \frac{24}{10} = \frac{12}{5} \] Thus, \( x = \frac{12}{5} \) or \( 2 \frac{2}{5} \) in mixed number form.