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Apply the distributive property to create an equivalent expression. (1)/(2)(6e-3f-(3)/(4))=

Apply the distributive property to create an equivalent expression.\newline12(6e−3f−34)= \frac{1}{2}\left(6 e-3 f-\frac{3}{4}\right)=

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Full solution

Q. Apply the distributive property to create an equivalent expression.\newline12(6e−3f−34)= \frac{1}{2}\left(6 e-3 f-\frac{3}{4}\right)=
  1. Identify Terms: Identify the terms inside the parentheses that will be distributed by the factor outside the parentheses.\newlineIn this case, the factor outside the parentheses is (12)(\frac{1}{2}), and the terms inside the parentheses are 6e6e, −3f-3f, and −(34)-(\frac{3}{4}).
  2. Apply Distributive Property: Apply the distributive property by multiplying the factor outside the parentheses with each term inside the parentheses.\newlineThis means we will perform the following operations: (12)×6e(\frac{1}{2}) \times 6e, (12)×−3f(\frac{1}{2}) \times -3f, and (12)×−(34)(\frac{1}{2}) \times -(\frac{3}{4}).
  3. Multiply 6e6e: Multiply (1/2)(1/2) by 6e6e.\newline(1/2)×6e=3e(1/2) \times 6e = 3e
  4. Multiply −3f-3f: Multiply (1/2)(1/2) by −3f-3f.(1/2)×−3f=−32f(1/2) \times -3f = -\frac{3}{2}f or −1.5f-1.5f
  5. Multiply −(34)-(\frac{3}{4}): Multiply (12)(\frac{1}{2}) by −(34)-(\frac{3}{4}).(12)×−(34)=−38(\frac{1}{2}) \times -(\frac{3}{4}) = -\frac{3}{8}
  6. Combine Results: Combine the results from steps 33, 44, and 55 to write the equivalent expression.\newlineThe equivalent expression is 3e−32f−38.3e - \frac{3}{2}f - \frac{3}{8}.

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