Multi Step Equations Worksheets - Math Monks - Free Printable

To solve the equations with variables on both sides, we will follow a systematic approach: simplify, isolate the variable, and solve. Let's go through each equation step by step.

---

Equation 1:

\[
-4q - 3 = -9 + 7q
\]

1. Move all terms involving \( q \) to one side:
\[
-4q - 7q = -9 + 3
\]
\[
-11q = -6
\]

2. Solve for \( q \):
\[
q = \frac{-6}{-11} = \frac{6}{11}
\]

Solution:
\[
\boxed{\frac{6}{11}}
\]

---

Equation 2:

\[
-p - 9p = 5p - 4
\]

1. Combine like terms on the left side:
\[
-10p = 5p - 4
\]

2. Move all terms involving \( p \) to one side:
\[
-10p - 5p = -4
\]
\[
-15p = -4
\]

3. Solve for \( p \):
\[
p = \frac{-4}{-15} = \frac{4}{15}
\]

Solution:
\[
\boxed{\frac{4}{15}}
\]

---

Equation 3:

\[
-4x - 14 = 7(-2 - 4x) + 4x
\]

1. Distribute the 7 on the right side:
\[
-4x - 14 = 7(-2) + 7(-4x) + 4x
\]
\[
-4x - 14 = -14 - 28x + 4x
\]

2. Combine like terms on the right side:
\[
-4x - 14 = -14 - 24x
\]

3. Move all terms involving \( x \) to one side and constants to the other:
\[
-4x + 24x = -14 + 14
\]
\[
20x = 0
\]

4. Solve for \( x \):
\[
x = 0
\]

Solution:
\[
\boxed{0}
\]

---

Equation 4:

\[
18 - 4n = -8 + 4(n - 2)
\]

1. Distribute the 4 on the right side:
\[
18 - 4n = -8 + 4n - 8
\]
\[
18 - 4n = -16 + 4n
\]

2. Move all terms involving \( n \) to one side and constants to the other:
\[
-4n - 4n = -16 - 18
\]
\[
-8n = -34
\]

3. Solve for \( n \):
\[
n = \frac{-34}{-8} = \frac{34}{8} = \frac{17}{4}
\]

Solution:
\[
\boxed{\frac{17}{4}}
\]

---

Equation 5:

\[
-6y + 7(1 - y) = -4(y - 4)
\]

1. Distribute the 7 and -4:
\[
-6y + 7 - 7y = -4y + 16
\]

2. Combine like terms on the left side:
\[
-13y + 7 = -4y + 16
\]

3. Move all terms involving \( y \) to one side and constants to the other:
\[
-13y + 4y = 16 - 7
\]
\[
-9y = 9
\]

4. Solve for \( y \):
\[
y = \frac{9}{-9} = -1
\]

Solution:
\[
\boxed{-1}
\]

---

Equation 6:

\[
4(a - 6) = -5a - (7 + 4a)
\]

1. Distribute the 4 and the negative sign:
\[
4a - 24 = -5a - 7 - 4a
\]

2. Combine like terms on the right side:
\[
4a - 24 = -9a - 7
\]

3. Move all terms involving \( a \) to one side and constants to the other:
\[
4a + 9a = -7 + 24
\]
\[
13a = 17
\]

4. Solve for \( a \):
\[
a = \frac{17}{13}
\]

Solution:
\[
\boxed{\frac{17}{13}}
\]

---

Equation 7:

\[
4r + 8 + 4 = -16 - 4r
\]

1. Combine like terms on the left side:
\[
4r + 12 = -16 - 4r
\]

2. Move all terms involving \( r \) to one side and constants to the other:
\[
4r + 4r = -16 - 12
\]
\[
8r = -28
\]

3. Solve for \( r \):
\[
r = \frac{-28}{8} = \frac{-7}{2}
\]

Solution:
\[
\boxed{-\frac{7}{2}}
\]

---

Equation 8:

\[
3v + 3 = 4v + 4
\]

1. Move all terms involving \( v \) to one side and constants to the other:
\[
3v - 4v = 4 - 3
\]
\[
-v = 1
\]

2. Solve for \( v \):
\[
v = -1
\]

Solution:
\[
\boxed{-1}
\]

---

Equation 9:

\[
6l + 2 + l - 3 = 8l - 8
\]

1. Combine like terms on the left side:
\[
7l - 1 = 8l - 8
\]

2. Move all terms involving \( l \) to one side and constants to the other:
\[
7l - 8l = -8 + 1
\]
\[
-l = -7
\]

3. Solve for \( l \):
\[
l = 7
\]

Solution:
\[
\boxed{7}
\]

---

Equation 10:

\[
40 - t = 4(-3 - 6t) + 6
\]

1. Distribute the 4 on the right side:
\[
40 - t = 4(-3) + 4(-6t) + 6
\]
\[
40 - t = -12 - 24t + 6
\]

2. Combine like terms on the right side:
\[
40 - t = -6 - 24t
\]

3. Move all terms involving \( t \) to one side and constants to the other:
\[
-t + 24t = -6 - 40
\]
\[
23t = -46
\]

4. Solve for \( t \):
\[
t = \frac{-46}{23} = -2
\]

Solution:
\[
\boxed{-2}
\]

---

Final Answers:

\[
\boxed{\frac{6}{11}, \frac{4}{15}, 0, \frac{17}{4}, -1, \frac{17}{13}, -\frac{7}{2}, -1, 7, -2}
\]