To evaluate the expression \( 4 \times \left( \frac{3}{4} - \frac{1}{2} \right) + 3 \times 6 \), we will follow the order of operations (parentheses, exponents, multiplication and division (from left to right), addition and subtraction (from left to right)).
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Evaluate the expression inside the parentheses: \[ \frac{3}{4} - \frac{1}{2} \] To subtract these fractions, we need a common denominator. The common denominator for 4 and 2 is 4. \[ \frac{1}{2} = \frac{2}{4} \] Now we can subtract: \[ \frac{3}{4} - \frac{2}{4} = \frac{1}{4} \]
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Substitute back into the expression: \[ 4 \times \left( \frac{1}{4} \right) + 3 \times 6 \]
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Perform the multiplication: \[ 4 \times \frac{1}{4} = 1 \] \[ 3 \times 6 = 18 \]
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Now add the results: \[ 1 + 18 = 19 \]
Thus, the value of the expression is \( \boxed{19} \).