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3(4x-5) - (2x+7)

show me the steps

1 answer

To simplify the expression \( 3(4x - 5) - (2x + 7) \), follow these steps:

  1. Distribute the \( 3 \) in the first term: \[ 3(4x) - 3(5) = 12x - 15 \]

  2. Distribute the negative sign across the second term: \[

    • (2x + 7) = -2x - 7 \]

  3. Now, combine the results from steps 1 and 2: \[ 12x - 15 - 2x - 7 \]

  4. Combine like terms (the \( x \) terms and the constant terms):

    • For the \( x \) terms: \[ 12x - 2x = 10x \]
    • For the constant terms: \[ -15 - 7 = -22 \]

  5. Therefore, the simplified expression is: \[ 10x - 22 \]

The final result is: \[ 10x - 22 \]