Grade 8 · Free math lesson
Algebra Foundations
After this lesson, you will be able to solve a basic algebra equation by finding the mystery number.
Practice Algebra Foundations freeSkills in this unit
Pick a skill to try three free questions on just that.
- Equations with variables on both sides
- Equations with the distributive property and fractions
- Solving and graphing linear inequalities
- Integer exponent rules
- Square roots and cube roots
- Scientific notation
- Rational and irrational numbers
- Literal equations
- Systems of linear equations
What Is an Equation?
An equation is like a balance scale — both sides must be equal. The letter (like x) is just a mystery number you need to find.
Example: x + 3 = 7 means: some number plus 3 equals 7. Your job is to find x.
Remember: Think of '=' as the middle of a seesaw — both sides must weigh the same!
Undo to Solve
To find x, you undo what is being done to it. If something is added, you subtract it from BOTH sides to keep the scale balanced.
Example: x + 3 = 7 → subtract 3 from both sides → x = 7 − 3 → x = 4.
Remember: Whatever you do to one side, do the SAME to the other side — always!
Check Your Answer
Plug your answer back into the original equation to see if both sides are equal. If they match, you got it right!
Example: We got x = 4. Check: 4 + 3 = 7 ✓ Both sides equal 7, so x = 4 is correct!
Remember: Always substitute back — it takes 5 seconds and saves you from a wrong answer!
Worked example
Solve: x + 9 = 15
- 1Step 1 — Identify what is happening to x. Here, 9 is being ADDED to x.
- 2Step 2 — Undo it: subtract 9 from BOTH sides. x + 9 − 9 = 15 − 9, which gives x = 6.
- 3Step 3 — Check: plug x = 6 back in. 6 + 9 = 15 ✓ Both sides match!
Answer: x = 6
The #1 mistake to avoid
Students only subtract from one side — for example, writing x + 9 − 9 = 15 but forgetting to subtract 9 from the right side too. Always do the same thing to BOTH sides!
Key takeaways
- An equation is a balanced scale — both sides are always equal.
- To solve for x, undo the operation by doing the opposite to BOTH sides.
- Always check your answer by plugging it back into the original equation.
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