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what the following is an equivalent simplified expression for 2(4x+7)-3(2x-4)

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To simplify the expression \( 2(4x + 7) - 3(2x - 4) \), follow these steps:

  1. Distribute \( 2 \) in the first term: \[ 2(4x + 7) = 8x + 14 \]

  2. Distribute \( -3 \) in the second term: \[ -3(2x - 4) = -6x + 12 \]

  3. Now, combine the results: \[ 8x + 14 - 6x + 12 \]

  4. Combine like terms:

    • Combine the \( x \) terms: \( 8x - 6x = 2x \)
    • Combine the constant terms: \( 14 + 12 = 26 \)

  5. Thus, the simplified expression is: \[ 2x + 26 \]

So, \( 2(4x + 7) - 3(2x - 4) \) simplifies to \( \boxed{2x + 26} \).