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show the work for all of theses

1) -5v + 2-(1-7v) + 11v
2) 6(2x-5y)-2(x+9y)
3) 8(p+1)-13p+9
4) 15-6(2m+1) -34+ 4m

1 answer

Sure! Let's solve each of the given expressions step by step.

1) \(-5v + 2 - (1 - 7v) + 11v\)

Step 1: Distribute the negative sign through the parenthesis: \[ -5v + 2 - 1 + 7v + 11v \]

Step 2: Combine like terms:

  • Combine the \(v\) terms: \(-5v + 7v + 11v = 13v\)
  • Combine the constant terms: \(2 - 1 = 1\)

Final answer: \[ 13v + 1 \]

2) \(6(2x - 5y) - 2(x + 9y)\)

Step 1: Distribute the constants: \[ 12x - 30y - 2x - 18y \]

Step 2: Combine like terms:

  • Combine the \(x\) terms: \(12x - 2x = 10x\)
  • Combine the \(y\) terms: \(-30y - 18y = -48y\)

Final answer: \[ 10x - 48y \]

3) \(8(p + 1) - 13p + 9\)

Step 1: Distribute the \(8\): \[ 8p + 8 - 13p + 9 \]

Step 2: Combine like terms:

  • Combine the \(p\) terms: \(8p - 13p = -5p\)
  • Combine the constant terms: \(8 + 9 = 17\)

Final answer: \[ -5p + 17 \]

4) \(15 - 6(2m + 1) - 34 + 4m\)

Step 1: Distribute the \(-6\): \[ 15 - 12m - 6 - 34 + 4m \]

Step 2: Combine like terms:

  • Combine the \(m\) terms: \(-12m + 4m = -8m\)
  • Combine the constant terms: \(15 - 6 - 34 = -25\)

Final answer: \[ -8m - 25 \]

So, to summarize, the final results are:

  1. \(13v + 1\)
  2. \(10x - 48y\)
  3. \(-5p + 17\)
  4. \(-8m - 25\)