Solved Name Date Period Kuta Software - Infinite Algebra 1 | Chegg.com - Free Printable

Problem: Solve each equation from the provided list.

We will solve each equation step by step. Let's go through them one by one.

---

#### 1) \( -20 = -4x - 6x \)

1. Combine like terms on the right-hand side:
\[
-20 = -10x
\]
2. Solve for \( x \) by dividing both sides by \(-10\):
\[
x = \frac{-20}{-10} = 2
\]

Solution: \( x = 2 \)

---

#### 2) \( 6 = 1 - 2n + 5 \)

1. Simplify the right-hand side:
\[
6 = 6 - 2n
\]
2. Subtract 6 from both sides:
\[
0 = -2n
\]
3. Solve for \( n \) by dividing both sides by \(-2\):
\[
n = 0
\]

Solution: \( n = 0 \)

---

#### 3) \( 8x - 2 = -9 + 7x \)

1. Subtract \( 7x \) from both sides to isolate \( x \)-terms on one side:
\[
8x - 7x - 2 = -9
\]
\[
x - 2 = -9
\]
2. Add 2 to both sides:
\[
x = -7
\]

Solution: \( x = -7 \)

---

#### 4) \( a + 5 = -5a + 5 \)

1. Subtract 5 from both sides:
\[
a = -5a
\]
2. Add \( 5a \) to both sides:
\[
6a = 0
\]
3. Solve for \( a \):
\[
a = 0
\]

Solution: \( a = 0 \)

---

#### 5) \( 4m - 4 = 4m \)

1. Subtract \( 4m \) from both sides:
\[
-4 = 0
\]
This is a contradiction, so there is no solution.

Solution: No solution

---

#### 6) \( p - 1 = 5p + 3p - 8 \)

1. Combine like terms on the right-hand side:
\[
p - 1 = 8p - 8
\]
2. Subtract \( p \) from both sides:
\[
-1 = 7p - 8
\]
3. Add 8 to both sides:
\[
7 = 7p
\]
4. Solve for \( p \) by dividing both sides by 7:
\[
p = 1
\]

Solution: \( p = 1 \)

---

#### 7) \( 5p - 14 = 8p + 4 \)

1. Subtract \( 5p \) from both sides:
\[
-14 = 3p + 4
\]
2. Subtract 4 from both sides:
\[
-18 = 3p
\]
3. Solve for \( p \) by dividing both sides by 3:
\[
p = -6
\]

Solution: \( p = -6 \)

---

#### 8) \( p - 4 = -9 + p \)

1. Subtract \( p \) from both sides:
\[
-4 = -9
\]
This is a contradiction, so there is no solution.

Solution: No solution

---

#### 9) \( -8 = -(x + 4) \)

1. Distribute the negative sign on the right-hand side:
\[
-8 = -x - 4
\]
2. Add 4 to both sides:
\[
-4 = -x
\]
3. Multiply both sides by \(-1\) to solve for \( x \):
\[
x = 4
\]

Solution: \( x = 4 \)

---

#### 10) \( 12 = -4(-6x - 3) \)

1. Distribute the \(-4\) on the right-hand side:
\[
12 = 24x + 12
\]
2. Subtract 12 from both sides:
\[
0 = 24x
\]
3. Solve for \( x \):
\[
x = 0
\]

Solution: \( x = 0 \)

---

#### 11) \( 14 = -(p - 8) \)

1. Distribute the negative sign on the right-hand side:
\[
14 = -p + 8
\]
2. Subtract 8 from both sides:
\[
6 = -p
\]
3. Multiply both sides by \(-1\) to solve for \( p \):
\[
p = -6
\]

Solution: \( p = -6 \)

---

#### 12) \( -(7 - 4x) = 9 \)

1. Distribute the negative sign on the left-hand side:
\[
-7 + 4x = 9
\]
2. Add 7 to both sides:
\[
4x = 16
\]
3. Solve for \( x \) by dividing both sides by 4:
\[
x = 4
\]

Solution: \( x = 4 \)

---

#### 13) \( -18 - 6k = 6(1 + 3k) \)

1. Distribute the 6 on the right-hand side:
\[
-18 - 6k = 6 + 18k
\]
2. Add \( 6k \) to both sides:
\[
-18 = 6 + 24k
\]
3. Subtract 6 from both sides:
\[
-24 = 24k
\]
4. Solve for \( k \) by dividing both sides by 24:
\[
k = -1
\]

Solution: \( k = -1 \)

---

#### 14) \( 5n + 34 = -2(1 - 7n) \)

1. Distribute the \(-2\) on the right-hand side:
\[
5n + 34 = -2 + 14n
\]
2. Subtract \( 5n \) from both sides:
\[
34 = -2 + 9n
\]
3. Add 2 to both sides:
\[
36 = 9n
\]
4. Solve for \( n \) by dividing both sides by 9:
\[
n = 4
\]

Solution: \( n = 4 \)

---

#### 15) \( 2(4x - 3) - 8 = 4 + 2x \)

1. Distribute the 2 on the left-hand side:
\[
8x - 6 - 8 = 4 + 2x
\]
2. Simplify the left-hand side:
\[
8x - 14 = 4 + 2x
\]
3. Subtract \( 2x \) from both sides:
\[
6x - 14 = 4
\]
4. Add 14 to both sides:
\[
6x = 18
\]
5. Solve for \( x \) by dividing both sides by 6:
\[
x = 3
\]

Solution: \( x = 3 \)

---

#### 16) \( 3n - 5 = -8(6 + 5n) \)

1. Distribute the \(-8\) on the right-hand side:
\[
3n - 5 = -48 - 40n
\]
2. Add \( 40n \) to both sides:
\[
43n - 5 = -48
\]
3. Add 5 to both sides:
\[
43n = -43
\]
4. Solve for \( n \) by dividing both sides by 43:
\[
n = -1
\]

Solution: \( n = -1 \)

---

#### 17) \( -(1 + 7x) - 6(-7 - x) = 36 \)

1. Distribute the negative signs:
\[
-1 - 7x + 42 + 6x = 36
\]
2. Combine like terms:
\[
-7x + 6x + 41 = 36
\]
\[
-x + 41 = 36
\]
3. Subtract 41 from both sides:
\[
-x = -5
\]
4. Solve for \( x \) by multiplying both sides by \(-1\):
\[
x = 5
\]

Solution: \( x = 5 \)

---

#### 18) \( -3(4x + 3) + 4(6x + 1) = 43 \)

1. Distribute the constants:
\[
-12x - 9 + 24x + 4 = 43
\]
2. Combine like terms:
\[
12x - 5 = 43
\]
3. Add 5 to both sides:
\[
12x = 48
\]
4. Solve for \( x \) by dividing both sides by 12:
\[
x = 4
\]

Solution: \( x = 4 \)

---

#### 19) \( 24a - 22 = -4(1 - 6a) \)

1. Distribute the \(-4\) on the right-hand side:
\[
24a - 22 = -4 + 24a
\]
2. Subtract \( 24a \) from both sides:
\[
-22 = -4
\]
This is a contradiction, so there is no solution.

Solution: No solution

---

#### 20) \( -5(1 - 5x) + 5(-8x - 2) = -4x - 8x \)

1. Distribute the constants:
\[
-5 + 25x - 40x - 10 = -12x
\]
2. Combine like terms:
\[
-15 - 15x = -12x
\]
3. Add \( 15x \) to both sides:
\[
-15 = 3x
\]
4. Solve for \( x \) by dividing both sides by 3:
\[
x = -5
\]

Solution: \( x = -5 \)

---

Final Answers:

\[
\boxed{
\begin{aligned}
1) & \ x = 2 \\
2) & \ n = 0 \\
3) & \ x = -7 \\
4) & \ a = 0 \\
5) & \ \text{No solution} \\
6) & \ p = 1 \\
7) & \ p = -6 \\
8) & \ \text{No solution} \\
9) & \ x = 4 \\
10) & \ x = 0 \\
11) & \ p = -6 \\
12) & \ x = 4 \\
13) & \ k = -1 \\
14) & \ n = 4 \\
15) & \ x = 3 \\
16) & \ n = -1 \\
17) & \ x = 5 \\
18) & \ x = 4 \\
19) & \ \text{No solution} \\
20) & \ x = -5 \\
\end{aligned}
}
\]