Simplify each expression. 1) $$ -5-3 x+1+x $$ 2) $$ -4 v+10 v $$ 3) $$ -2-5 b+9 b $$ 4) $$ -4 b-8 b $$ 5) $$ n+3+n-9 $$ 6) $$ 6(5 x+8) $$ 7) $$ 10(10 n-6) $$ 8) $$ -5(x-4) $$ 9) $$ 4(2 n+2) $$ 10) $$ -6(v-8) $$ 11) $$ -7(5-4 a)+1 $$ 12) $$ -5(2-9 v)+6 v $$ 13) $$ 4 b-3(b-7) $$ 14) $$ 2(-10 x-4)+6 $$ 15) $$ 9 n+5(n-2) $$ 16) $$ -2(-7+10 a)-10(7 a-1) $$ 17) $$ -4(n+4)-3(4+n) $$ 18) $$ 5(7 x-6)-(2+9 x) $$

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UpStudy AI · Accepted Answer

Sure, let's simplify each of the given expressions step by step:

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**1) $$ -5 - 3x + 1 + x $$**
$$
\begin{align*}
-5 + 1 &= -4 \
-3x + x &= -2x \
\text{Simplified: } & -2x - 4
\end{align*}
$$

---

**2) $$ -4v + 10v $$**
$$
\begin{align*}
-4v + 10v &= 6v \
\text{Simplified: } & 6v
\end{align*}
$$

---

**3) $$ -2 - 5b + 9b $$**
$$
\begin{align*}
-5b + 9b &= 4b \
\text{Constant: } & -2 \
\text{Simplified: } & 4b - 2
\end{align*}
$$

---

**4) $$ -4b - 8b $$**
$$
\begin{align*}
-4b - 8b &= -12b \
\text{Simplified: } & -12b
\end{align*}
$$

---

**5) $$ n + 3 + n - 9 $$**
$$
\begin{align*}
n + n &= 2n \
3 - 9 &= -6 \
\text{Simplified: } & 2n - 6
\end{align*}
$$

---

**6) $$ 6(5x + 8) $$**
$$
\begin{align*}
6 \times 5x &= 30x \
6 \times 8 &= 48 \
\text{Simplified: } & 30x + 48
\end{align*}
$$

---

**7) $$ 10(10n - 6) $$**
$$
\begin{align*}
10 \times 10n &= 100n \
10 \times (-6) &= -60 \
\text{Simplified: } & 100n - 60
\end{align*}
$$

---

**8) $$ -5(x - 4) $$**
$$
\begin{align*}
-5 \times x &= -5x \
-5 \times (-4) &= 20 \
\text{Simplified: } & -5x + 20
\end{align*}
$$

---

**9) $$ 4(2n + 2) $$**
$$
\begin{align*}
4 \times 2n &= 8n \
4 \times 2 &= 8 \
\text{Simplified: } & 8n + 8
\end{align*}
\}

---

**10) $$ -6(v - 8) $$**
\[
\begin{align*}
-6 \times v &= -6v \
-6 \times (-8) &= 48 \
\text{Simplified: } & -6v + 48
\end{align*}
$$

---

**11) $$ -7(5 - 4a) + 1 $$**
$$
\begin{align*}
-7 \times 5 &= -35 \
-7 \times (-4a) &= 28a \
\text{Adding the constant: } & -35 + 1 = -34 \
\text{Simplified: } & 28a - 34
\end{align*}
$$

---

**12) $$ -5(2 - 9v) + 6v $$**
$$
\begin{align*}
-5 \times 2 &= -10 \
-5 \times (-9v) &= 45v \
\text{Adding $$ 6v $$: } & 45v + 6v = 51v \
\text{Simplified: } & 51v - 10
\end{align*}
$$

---

**13) $$ 4b - 3(b - 7) $$**
$$
\begin{align*}
-3 \times b &= -3b \
-3 \times (-7) &= 21 \
\text{Combine with $$ 4b $$: } & 4b - 3b = b \
\text{Simplified: } & b + 21
\end{align*}
$$

---

**14) $$ 2(-10x - 4) + 6 $$**
$$
\begin{align*}
2 \times (-10x) &= -20x \
2 \times (-4) &= -8 \
\text{Adding 6: } & -8 + 6 = -2 \
\text{Simplified: } & -20x - 2
\end{align*}
$$

---

**15) $$ 9n + 5(n - 2) $$**
$$
\begin{align*}
5 \times n &= 5n \
5 \times (-2) &= -10 \
\text{Combine with $$ 9n $$: } & 9n + 5n = 14n \
\text{Simplified: } & 14n - 10
\end{align*}
\}

---

**16) $$ -2(-7 + 10a) - 10(7a - 1) $$**
\[
\begin{align*}
-2 \times (-7) &= 14 \
-2 \times 10a &= -20a \
-10 \times 7a &= -70a \
-10 \times (-1) &= 10 \
\text{Combine constants and like terms: } & 14 + 10 = 24 \
& -20a - 70a = -90a \
\text{Simplified: } & 24 - 90a
\end{align*}
$$

---

**17) $$ -4(n + 4) - 3(4 + n) $$**
\[
\begin{align*}
-4 \times n &= -4n \
-4 \times 4 &= -16 \
-3 \times 4 &= -12 \
-3 \times n &= -3n \
\text{Combine like terms: } & -4n - 3n = -7n \
& -16 - 12 = -28 \
\text{Simplified: } & -7n - 28
\end{align*}
\}

---

**18) $$ 5(7x - 6) - (2 + 9x) $$**
\[
\begin{align*}
5 \times 7x &= 35x \
5 \times (-6) &= -30 \
-1 \times 2 &= -2 \
-1 \times 9x &= -9x \
\text{Combine like terms: } & 35x - 9x = 26x \
& -30 - 2 = -32 \
\text{Simplified: } & 26x - 32
\end{align*}
\}

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**Summary of Simplified Expressions:**

1. $$ -2x - 4 $$
2. $$ 6v $$
3. $$ 4b - 2 $$
4. $$ -12b $$
5. $$ 2n - 6 $$
6. $$ 30x + 48 $$
7. $$ 100n - 60 $$
8. $$ -5x + 20 $$
9. $$ 8n + 8 $$
10. $$ -6v + 48 $$
11. $$ 28a - 34 $$
12. $$ 51v - 10 $$
13. $$ b + 21 $$
14. $$ -20x - 2 $$
15. $$ 14n - 10 $$
16. $$ 24 - 90a $$
17. $$ -7n - 28 $$
18. $$ 26x - 32 $$

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Feel free to ask if you need further explanations on any of these simplifications!
1. $$ -2x - 4 $$ 2. $$ 6v $$ 3. $$ 4b - 2 $$ 4. $$ -12b $$ 5. $$ 2n - 6 $$ 6. $$ 30x + 48 $$ 7. $$ 100n - 60 $$ 8. $$ -5x + 20 $$ 9. $$ 8n + 8 $$ 10. $$ -6v + 48 $$ 11. $$ 28a - 34 $$ 12. $$ 51v - 10 $$ 13. $$ b + 21 $$ 14. $$ -20x - 2 $$ 15. $$ 14n - 10 $$ 16. $$ 24 - 90a $$ 17. $$ -7n - 28 $$ 18. $$ 26x - 32 $$

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