Algebra Worksheets - Free Printable

It looks like you've uploaded an image of a completed math worksheet titled "Solve the Equation Sheet 1 Answers" from math-salamanders.com, which provides solutions to 25 simple algebraic equations. The worksheet includes three columns:

- SOLVE: The equation to solve.
- WORKING: (Left blank — presumably for students to show their steps.)
- ANSWER: The correct solution.

Below is a detailed explanation of how to solve each type of equation, using examples from the list. Since the answers are already provided, I'll explain the methodology behind solving these equations step by step.

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🔧 General Strategy:

To solve one-step equations, use inverse operations:
- Addition ↔ Subtraction
- Multiplication ↔ Division

The goal is to isolate the variable on one side of the equation.

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✔ Example Walkthroughs:

#### 1) \( a - 1 = 7 \)
Add 1 to both sides:
\[
a = 7 + 1 = 8
\]
✔ Answer: \( a = 8 \)

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#### 2) \( b + 2 = 12 \)
Subtract 2 from both sides:
\[
b = 12 - 2 = 10
\]
✔ Answer: \( b = 10 \)

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#### 3) \( 2 \times c = 14 \)
Divide both sides by 2:
\[
c = 14 \div 2 = 7
\]
✔ Answer: \( c = 7 \)

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#### 4) \( d + 4 = 14 \)
Subtract 4:
\[
d = 14 - 4 = 10
\]
✔ Answer: \( d = 10 \)

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#### 5) \( e - 2 = 5 \)
Add 2:
\[
e = 5 + 2 = 7
\]
✔ Answer: \( e = 7 \)

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#### 6) \( f \times 3 = 12 \)
Divide by 3:
\[
f = 12 \div 3 = 4
\]
✔ Answer: \( f = 4 \)

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#### 7) \( q + 4 = 17 \)
Subtract 4:
\[
q = 17 - 4 = 13
\]
✔ Answer: \( q = 13 \)

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#### 8) \( h - 2 = 12 \)
Add 2:
\[
h = 12 + 2 = 14
\]
✔ Answer: \( h = 14 \)

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#### 9) \( 10 - i = 3 \)
Rewrite: \( 10 - i = 3 \Rightarrow i = 10 - 3 = 7 \)
Or: subtract 10 from both sides: \( -i = 3 - 10 = -7 \), then multiply by -1: \( i = 7 \)
✔ Answer: \( i = 7 \)

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#### 10) \( j - 8 = 7 \)
Add 8:
\[
j = 7 + 8 = 15
\]
✔ Answer: \( j = 15 \)

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#### 11) \( 2k = 8 \)
Divide by 2:
\[
k = 8 \div 2 = 4
\]
✔ Answer: \( k = 4 \)

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#### 12) \( l - 6 = 11 \)
Add 6:
\[
l = 11 + 6 = 17
\]
✔ Answer: \( l = 17 \)

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#### 13) \( 12 - m = 2 \)
Rewrite: \( m = 12 - 2 = 10 \)
✔ Answer: \( m = 10 \)

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#### 14) \( 4n = 28 \)
Divide by 4:
\[
n = 28 \div 4 = 7
\]
✔ Answer: \( n = 7 \)

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#### 15) \( o \div 2 = 6 \)
Multiply both sides by 2:
\[
o = 6 \times 2 = 12
\]
✔ Answer: \( o = 12 \)

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#### 16) \( p \div 5 = 4 \)
Multiply by 5:
\[
p = 4 \times 5 = 20
\]
✔ Answer: \( p = 20 \)

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#### 17) \( q \div 4 = 6 \)
Multiply by 4:
\[
q = 6 \times 4 = 24
\]
✔ Answer: \( q = 24 \)

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#### 18) \( 5r = 30 \)
Divide by 5:
\[
r = 30 \div 5 = 6
\]
✔ Answer: \( r = 6 \)

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#### 19) \( s - 12 = 7 \)
Add 12:
\[
s = 7 + 12 = 19
\]
✔ Answer: \( s = 19 \)

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#### 20) \( 20 - t = 11 \)
Rewrite: \( t = 20 - 11 = 9 \)
✔ Answer: \( t = 9 \)

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#### 21) \( 6u = 24 \)
Divide by 6:
\[
u = 24 \div 6 = 4
\]
✔ Answer: \( u = 4 \)

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#### 22) \( v - 6 = 3 \)
Add 6:
\[
v = 3 + 6 = 9
\]
✔ Answer: \( v = 9 \)

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#### 23) \( 20 \div w = 4 \)
Rewrite: \( \frac{20}{w} = 4 \Rightarrow w = 20 \div 4 = 5 \)
✔ Answer: \( w = 5 \)

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#### 24) \( 7x = 14 \)
Divide by 7:
\[
x = 14 \div 7 = 2
\]
✔ Answer: \( x = 2 \)

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#### 25) \( 5 - y = -1 \)
Rewrite: \( 5 - y = -1 \Rightarrow -y = -1 - 5 = -6 \Rightarrow y = 6 \)
Or: add \( y \) to both sides and add 1: \( 5 + 1 = y \Rightarrow y = 6 \)
✔ Answer: \( y = 6 \)

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📌 Summary:

All equations are one-step linear equations, solved by applying the inverse operation to isolate the variable.

Each answer matches the given solution in the image.

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✔ Final Note:

This worksheet is designed for beginners learning algebra, focusing on understanding how to manipulate equations to find unknown values.

If you'd like, I can generate a student-friendly version with working steps filled in or create similar problems for practice!