show the work for all of theses

Question

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

Answer 1

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: $$13v+1$$

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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: $$10x-48y$$

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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: $$-5p+17$$

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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: $$-8m-25$$

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So, to summarize, the final results are:

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