Basic Algebra Worksheets - Free Printable

To solve the given equations and determine the value of each variable, we will evaluate each equation step by step. Here is the solution for each problem:

---

Equation Sheet 3

#### 1. \( x + 5 = 12 \)
- Subtract 5 from both sides:
\[
x = 12 - 5
\]
\[
x = 7
\]

#### 2. \( k - 7 = 10 \)
- Add 7 to both sides:
\[
k = 10 + 7
\]
\[
k = 17
\]

#### 3. \( 4x + 8 = 20 \)
- Subtract 8 from both sides:
\[
4x = 20 - 8
\]
\[
4x = 12
\]
- Divide both sides by 4:
\[
x = \frac{12}{4}
\]
\[
x = 3
\]

#### 4. \( 6y - 9 = 15 \)
- Add 9 to both sides:
\[
6y = 15 + 9
\]
\[
6y = 24
\]
- Divide both sides by 6:
\[
y = \frac{24}{6}
\]
\[
y = 4
\]

#### 5. \( 7z + 0 = 21 \)
- Simplify the equation (since adding 0 does not change the value):
\[
7z = 21
\]
- Divide both sides by 7:
\[
z = \frac{21}{7}
\]
\[
z = 3
\]

#### 6. \( 16 - 2m = 10 \)
- Subtract 16 from both sides:
\[
-2m = 10 - 16
\]
\[
-2m = -6
\]
- Divide both sides by -2:
\[
m = \frac{-6}{-2}
\]
\[
m = 3
\]

#### 7. \( 3p + 1 = 10 \)
- Subtract 1 from both sides:
\[
3p = 10 - 1
\]
\[
3p = 9
\]
- Divide both sides by 3:
\[
p = \frac{9}{3}
\]
\[
p = 3
\]

#### 8. \( 5(q - 1) = 20 \)
- Distribute the 5:
\[
5q - 5 = 20
\]
- Add 5 to both sides:
\[
5q = 20 + 5
\]
\[
5q = 25
\]
- Divide both sides by 5:
\[
q = \frac{25}{5}
\]
\[
q = 5
\]

#### 9. \( 9r + 8 = 80 \)
- Subtract 8 from both sides:
\[
9r = 80 - 8
\]
\[
9r = 72
\]
- Divide both sides by 9:
\[
r = \frac{72}{9}
\]
\[
r = 8
\]

#### 10. \( s - 12 = 25 \)
- Add 12 to both sides:
\[
s = 25 + 12
\]
\[
s = 37
\]

#### 11. \( 2t + 3 = 15 \)
- Subtract 3 from both sides:
\[
2t = 15 - 3
\]
\[
2t = 12
\]
- Divide both sides by 2:
\[
t = \frac{12}{2}
\]
\[
t = 6
\]

#### 12. \( u + 0.5 = 3.5 \)
- Subtract 0.5 from both sides:
\[
u = 3.5 - 0.5
\]
\[
u = 3
\]

#### 13. \( v - 7 = -10 \)
- Add 7 to both sides:
\[
v = -10 + 7
\]
\[
v = -3
\]

#### 14. \( w + 15 = 20 \)
- Subtract 15 from both sides:
\[
w = 20 - 15
\]
\[
w = 5
\]

#### 15. \( (y - 2) \times 3 = 15 \)
- Divide both sides by 3:
\[
y - 2 = \frac{15}{3}
\]
\[
y - 2 = 5
\]
- Add 2 to both sides:
\[
y = 5 + 2
\]
\[
y = 7
\]

#### 16. \( z + 7 = 14 \)
- Subtract 7 from both sides:
\[
z = 14 - 7
\]
\[
z = 7
\]

#### 17. \( 2a + 3 = 13 \)
- Subtract 3 from both sides:
\[
2a = 13 - 3
\]
\[
2a = 10
\]
- Divide both sides by 2:
\[
a = \frac{10}{2}
\]
\[
a = 5
\]

#### 18. \( b^2 = 100 \)
- Take the square root of both sides:
\[
b = \pm \sqrt{100}
\]
\[
b = \pm 10
\]

#### 19. \( c \times 2 = 18 \)
- Divide both sides by 2:
\[
c = \frac{18}{2}
\]
\[
c = 9
\]

#### 20. \( 3d + 2 = 8 \)
- Subtract 2 from both sides:
\[
3d = 8 - 2
\]
\[
3d = 6
\]
- Divide both sides by 3:
\[
d = \frac{6}{3}
\]
\[
d = 2
\]

---

Final Answers:

\[
\boxed{
\begin{array}{ll}
1. & x = 7 \\
2. & k = 17 \\
3. & x = 3 \\
4. & y = 4 \\
5. & z = 3 \\
6. & m = 3 \\
7. & p = 3 \\
8. & q = 5 \\
9. & r = 8 \\
10. & s = 37 \\
11. & t = 6 \\
12. & u = 3 \\
13. & v = -3 \\
14. & w = 5 \\
15. & y = 7 \\
16. & z = 7 \\
17. & a = 5 \\
18. & b = \pm 10 \\
19. & c = 9 \\
20. & d = 2 \\
\end{array}
}
\]