Two-step equation worksheet answer key with integer solutions.

The image provided is a math worksheet titled "Two Step Equation - Integers," which involves solving two-step equations with integers. Below, I will explain the solution process for each equation step by step.

---

Equation 1: \( 2x + 8 = -6 \)

1. Subtract 8 from both sides:
\[
2x + 8 - 8 = -6 - 8
\]
\[
2x = -14
\]

2. Divide both sides by 2:
\[
\frac{2x}{2} = \frac{-14}{2}
\]
\[
x = -7
\]

Solution: \( x = -7 \)

---

Equation 2: \( 3a - 9 = -30 \)

1. Add 9 to both sides:
\[
3a - 9 + 9 = -30 + 9
\]
\[
3a = -21
\]

2. Divide both sides by 3:
\[
\frac{3a}{3} = \frac{-21}{3}
\]
\[
a = -7
\]

Solution: \( a = -7 \)

---

Equation 3: \( -20 = 4m + 40 \)

1. Subtract 40 from both sides:
\[
-20 - 40 = 4m + 40 - 40
\]
\[
-60 = 4m
\]

2. Divide both sides by 4:
\[
\frac{-60}{4} = \frac{4m}{4}
\]
\[
m = -15
\]

Solution: \( m = -15 \)

---

Equation 4: \( -17 = 11 - 4p \)

1. Subtract 11 from both sides:
\[
-17 - 11 = 11 - 4p - 11
\]
\[
-28 = -4p
\]

2. Divide both sides by -4:
\[
\frac{-28}{-4} = \frac{-4p}{-4}
\]
\[
p = 7
\]

Solution: \( p = 7 \)

---

Equation 5: \( 25 - 6n = -11 \)

1. Subtract 25 from both sides:
\[
25 - 6n - 25 = -11 - 25
\]
\[
-6n = -36
\]

2. Divide both sides by -6:
\[
\frac{-6n}{-6} = \frac{-36}{-6}
\]
\[
n = 6
\]

Solution: \( n = 6 \)

---

Equation 6: \( 7t + 28 = -14 \)

1. Subtract 28 from both sides:
\[
7t + 28 - 28 = -14 - 28
\]
\[
7t = -42
\]

2. Divide both sides by 7:
\[
\frac{7t}{7} = \frac{-42}{7}
\]
\[
t = -6
\]

Solution: \( t = -6 \)

---

Equation 7: \( -8b - 29 = 43 \)

1. Add 29 to both sides:
\[
-8b - 29 + 29 = 43 + 29
\]
\[
-8b = 72
\]

2. Divide both sides by -8:
\[
\frac{-8b}{-8} = \frac{72}{-8}
\]
\[
b = -9
\]

Solution: \( b = -9 \)

---

Equation 8: \( -45 = -3f + 15 \)

1. Subtract 15 from both sides:
\[
-45 - 15 = -3f + 15 - 15
\]
\[
-60 = -3f
\]

2. Divide both sides by -3:
\[
\frac{-60}{-3} = \frac{-3f}{-3}
\]
\[
f = 20
\]

Solution: \( f = 20 \)

---

Equation 9: \( 9c - 29 = 34 \)

1. Add 29 to both sides:
\[
9c - 29 + 29 = 34 + 29
\]
\[
9c = 63
\]

2. Divide both sides by 9:
\[
\frac{9c}{9} = \frac{63}{9}
\]
\[
c = 7
\]

Solution: \( c = 7 \)

---

Equation 10: \( 33 = -22 - 11e \)

1. Add 22 to both sides:
\[
33 + 22 = -22 - 11e + 22
\]
\[
55 = -11e
\]

2. Divide both sides by -11:
\[
\frac{55}{-11} = \frac{-11e}{-11}
\]
\[
e = -5
\]

Solution: \( e = -5 \)

---

Equation 11: \( 55 - 3x = -20 \)

1. Subtract 55 from both sides:
\[
55 - 3x - 55 = -20 - 55
\]
\[
-3x = -75
\]

2. Divide both sides by -3:
\[
\frac{-3x}{-3} = \frac{-75}{-3}
\]
\[
x = 25
\]

Solution: \( x = 25 \)

---

Equation 12: \( -16 = -5n - 66 \)

1. Add 66 to both sides:
\[
-16 + 66 = -5n - 66 + 66
\]
\[
50 = -5n
\]

2. Divide both sides by -5:
\[
\frac{50}{-5} = \frac{-5n}{-5}
\]
\[
n = -10
\]

Solution: \( n = -10 \)

---

Final Answer:

\[
\boxed{
\begin{aligned}
&x = -7, \quad a = -7, \quad m = -15, \quad p = 7, \quad n = 6, \quad t = -6, \\
&b = -9, \quad f = 20, \quad c = 7, \quad e = -5, \quad x = 25, \quad n = -10
\end{aligned}
}
\]