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Simplify the following expressions.

1. 8 -3(2x - 5)
2. 2(5x + 4) -3
3. 5(3x + 4) -4

1 answer

Let's simplify each expression step by step.

  1. Expression: \( 8 - 3(2x - 5) \)

    Step 1: Distribute \(-3\) into \((2x - 5)\): \[ 8 - 3(2x) + 3(5) = 8 - 6x + 15 \]

    Step 2: Combine like terms: \[ 8 + 15 - 6x = 23 - 6x \]

    Simplified Expression: \( 23 - 6x \)

  2. Expression: \( 2(5x + 4) - 3 \)

    Step 1: Distribute \(2\) into \((5x + 4)\): \[ 2(5x) + 2(4) - 3 = 10x + 8 - 3 \]

    Step 2: Combine like terms: \[ 10x + 8 - 3 = 10x + 5 \]

    Simplified Expression: \( 10x + 5 \)

  3. Expression: \( 5(3x + 4) - 4 \)

    Step 1: Distribute \(5\) into \((3x + 4)\): \[ 5(3x) + 5(4) - 4 = 15x + 20 - 4 \]

    Step 2: Combine like terms: \[ 15x + 20 - 4 = 15x + 16 \]

    Simplified Expression: \( 15x + 16 \)

In summary, the simplified expressions are:

  1. \( 23 - 6x \)
  2. \( 10x + 5 \)
  3. \( 15x + 16 \)