Basic Algebra Worksheets - Free Printable

To solve the given equations and find the values of the variables, we will go through each equation step by step. Here are the solutions:

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1) \( 4a = 20 \)

- Working: Divide both sides by 4.
\[
a = \frac{20}{4} = 5
\]
- Answer: \( a = 5 \)

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2) \( b - 7 = 8 \)

- Working: Add 7 to both sides.
\[
b = 8 + 7 = 15
\]
- Answer: \( b = 15 \)

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3) \( 2c - 1 = 11 \)

- Working: Add 1 to both sides, then divide by 2.
\[
2c = 11 + 1 = 12
\]
\[
c = \frac{12}{2} = 6
\]
- Answer: \( c = 6 \)

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4) \( 10 = d + 6 \)

- Working: Subtract 6 from both sides.
\[
d = 10 - 6 = 4
\]
- Answer: \( d = 4 \)

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5) \( 18 = 3e \)

- Working: Divide both sides by 3.
\[
e = \frac{18}{3} = 6
\]
- Answer: \( e = 6 \)

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6) \( f - 7 = 4 + 4 \)

- Working: Simplify the right side, then add 7 to both sides.
\[
f - 7 = 8
\]
\[
f = 8 + 7 = 15
\]
- Answer: \( f = 15 \)

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7) \( 2g = 7 - 5 \)

- Working: Simplify the right side, then divide by 2.
\[
2g = 2
\]
\[
g = \frac{2}{2} = 1
\]
- Answer: \( g = 1 \)

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8) \( 16 - 2h = 0 \)

- Working: Subtract 16 from both sides, then divide by -2.
\[
-2h = -16
\]
\[
h = \frac{-16}{-2} = 8
\]
- Answer: \( h = 8 \)

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9) \( 2(i + 1) = 18 \)

- Working: Divide both sides by 2, then subtract 1.
\[
i + 1 = \frac{18}{2} = 9
\]
\[
i = 9 - 1 = 8
\]
- Answer: \( i = 8 \)

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10) \( 3(j - 1) = 21 \)

- Working: Divide both sides by 3, then add 1.
\[
j - 1 = \frac{21}{3} = 7
\]
\[
j = 7 + 1 = 8
\]
- Answer: \( j = 8 \)

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11) \( 5(k + 2) = 45 \)

- Working: Divide both sides by 5, then subtract 2.
\[
k + 2 = \frac{45}{5} = 9
\]
\[
k = 9 - 2 = 7
\]
- Answer: \( k = 7 \)

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12) \( 4(l - 6) = 16 \)

- Working: Divide both sides by 4, then add 6.
\[
l - 6 = \frac{16}{4} = 4
\]
\[
l = 4 + 6 = 10
\]
- Answer: \( l = 10 \)

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13) \( 2m - 5 = 11 \)

- Working: Add 5 to both sides, then divide by 2.
\[
2m = 11 + 5 = 16
\]
\[
m = \frac{16}{2} = 8
\]
- Answer: \( m = 8 \)

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14) \( \frac{1}{2}n + 1 = 8 \)

- Working: Subtract 1 from both sides, then multiply by 2.
\[
\frac{1}{2}n = 8 - 1 = 7
\]
\[
n = 7 \times 2 = 14
\]
- Answer: \( n = 14 \)

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15) \( 20 \div o = 4 \)

- Working: Rewrite as \( \frac{20}{o} = 4 \), then solve for \( o \).
\[
o = \frac{20}{4} = 5
\]
- Answer: \( o = 5 \)

---

16) \( p \div 7 = 3 \)

- Working: Rewrite as \( \frac{p}{7} = 3 \), then solve for \( p \).
\[
p = 3 \times 7 = 21
\]
- Answer: \( p = 21 \)

---

17) \( q \div 6 = 5 \)

- Working: Rewrite as \( \frac{q}{6} = 5 \), then solve for \( q \).
\[
q = 5 \times 6 = 30
\]
- Answer: \( q = 30 \)

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18) \( 4(r + 2) = 24 \)

- Working: Divide both sides by 4, then subtract 2.
\[
r + 2 = \frac{24}{4} = 6
\]
\[
r = 6 - 2 = 4
\]
- Answer: \( r = 4 \)

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19) \( 20 = 5(s - 3) \)

- Working: Divide both sides by 5, then add 3.
\[
s - 3 = \frac{20}{5} = 4
\]
\[
s = 4 + 3 = 7
\]
- Answer: \( s = 7 \)

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20) \( \frac{1}{2}t + 7 = 13 \)

- Working: Subtract 7 from both sides, then multiply by 2.
\[
\frac{1}{2}t = 13 - 7 = 6
\]
\[
t = 6 \times 2 = 12
\]
- Answer: \( t = 12 \)

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21) \( u^2 = 36 \)

- Working: Take the square root of both sides.
\[
u = \pm \sqrt{36} = \pm 6
\]
- Answer: \( u = 6 \) or \( u = -6 \)

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22) \( v^2 = 100 \)

- Working: Take the square root of both sides.
\[
v = \pm \sqrt{100} = \pm 10
\]
- Answer: \( v = 10 \) or \( v = -10 \)

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23) \( w = \sqrt{25} \)

- Working: The square root of 25 is 5.
\[
w = 5
\]
- Answer: \( w = 5 \)

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24) \( 3x = 20 - 8 \)

- Working: Simplify the right side, then divide by 3.
\[
3x = 12
\]
\[
x = \frac{12}{3} = 4
\]
- Answer: \( x = 4 \)

---

25) \( 18 - 4y = 2 \)

- Working: Subtract 18 from both sides, then divide by -4.
\[
-4y = 2 - 18 = -16
\]
\[
y = \frac{-16}{-4} = 4
\]
- Answer: \( y = 4 \)

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Final Answers:

\[
\boxed{
\begin{array}{ll}
1) & a = 5 \\
2) & b = 15 \\
3) & c = 6 \\
4) & d = 4 \\
5) & e = 6 \\
6) & f = 15 \\
7) & g = 1 \\
8) & h = 8 \\
9) & i = 8 \\
10) & j = 8 \\
11) & k = 7 \\
12) & l = 10 \\
13) & m = 8 \\
14) & n = 14 \\
15) & o = 5 \\
16) & p = 21 \\
17) & q = 30 \\
18) & r = 4 \\
19) & s = 7 \\
20) & t = 12 \\
21) & u = 6 \text{ or } u = -6 \\
22) & v = 10 \text{ or } v = -10 \\
23) & w = 5 \\
24) & x = 4 \\
25) & y = 4 \\
\end{array}
}
\]