Algebraic equations might look scary with all those letters, but...
Maths135 views·Updated 6 Sept 2026·2 pagesUnderstanding Algebraic Equations: One-Letter Variable Problems
C Townsend@ctownsend_mcpv
1
of 2
Getting Started with Single Variable Equations
Think of algebraic equations as detective work - you're hunting for the mystery number hiding behind a letter. When you see something like x + 3 = 10, you're really being asked "what number plus 3 equals 10?"
The golden rule is simple: do the opposite of what's been done to your unknown letter. If something's been added, subtract it. If something's been subtracted, add it back.
Let's crack x + 3 = 10. Since 3 was added to x, we subtract 3 from the other side: 10 - 3 = 7. So x = 7! Don't worry if the equation looks backwards like 14 = a - 5 - just flip it around to a - 5 = 14, then add 5 to both sides to get a = 19.
Quick Tip: Always check your answer by plugging it back into the original equation!
2
of 2
Tackling Multiplication and Division
Now we're dealing with multiplication and division, but honestly, it's just as straightforward. The same "do the opposite" rule applies - if your unknown is being multiplied, you divide, and vice versa.
Take b × 3 = 18. Since b is multiplied by 3, we divide both sides by 3: 18 ÷ 3 = 6. Therefore b = 6! Easy peasy.
When you see something like 8 = f ÷ 2, flip it if it helps: f ÷ 2 = 8. Since f is being divided by 2, multiply both sides by 2: 8 × 2 = 16, so f = 16.
Remember: Multiplication and division are opposites, just like addition and subtraction!
The beauty of algebra is that once you've mastered this "opposite operation" technique, you can solve loads of different equations using the exact same method.
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Maths135 views·Updated 6 Sept 2026·2 pagesUnderstanding Algebraic Equations: One-Letter Variable Problems
C Townsend@ctownsend_mcpv
Algebraic equations might look scary with all those letters, but they're actually just puzzles asking "what number am I?" Once you learn the simple trick of doing the opposite operation, you'll crack these equations every time!
1
of 2
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Getting Started with Single Variable Equations
Think of algebraic equations as detective work - you're hunting for the mystery number hiding behind a letter. When you see something like x + 3 = 10, you're really being asked "what number plus 3 equals 10?"
The golden rule is simple: do the opposite of what's been done to your unknown letter. If something's been added, subtract it. If something's been subtracted, add it back.
Let's crack x + 3 = 10. Since 3 was added to x, we subtract 3 from the other side: 10 - 3 = 7. So x = 7! Don't worry if the equation looks backwards like 14 = a - 5 - just flip it around to a - 5 = 14, then add 5 to both sides to get a = 19.
Quick Tip: Always check your answer by plugging it back into the original equation!
2
of 2Sign up to see the content. It's free!
- Access to all documents
- Improve your grades
- Join milions of students
By signing up you accept Terms of Service and Privacy Policy
Tackling Multiplication and Division
Now we're dealing with multiplication and division, but honestly, it's just as straightforward. The same "do the opposite" rule applies - if your unknown is being multiplied, you divide, and vice versa.
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When you see something like 8 = f ÷ 2, flip it if it helps: f ÷ 2 = 8. Since f is being divided by 2, multiply both sides by 2: 8 × 2 = 16, so f = 16.
Remember: Multiplication and division are opposites, just like addition and subtraction!
The beauty of algebra is that once you've mastered this "opposite operation" technique, you can solve loads of different equations using the exact same method.
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Our AI Companion is a student-focused AI tool that offers more than just answers. Built on millions of Knowunity resources, it provides relevant information, personalised study plans, quizzes, and content directly in the chat, adapting to your individual learning journey.
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