Solve 4x − 7 = 9
- Add 7 to both sides: 4x = 16.
- Divide both sides by 4: x = 4.
- Check: 4(4) − 7 = 16 − 7 = 9.
Solving equations with balance
Find an unknown by keeping both sides equal at every step.
Lesson 03 · Start where you need
Your learning goal
Solve equations of the form ax + b = c using inverse operations and verify the solution.
An equation is a claim of equality
In 3x + 5 = 20, the expressions on the two sides must have the same value. Solving means finding values of x that make that claim true. An equality symbol is not an instruction to write the next calculation; it says the two expressions are equal.
Words worth knowing
- Inverse operation
- An operation that undoes another operation.
- Solution
- A value that makes the original equation true.
- Preservation of equality
- Changing both sides in a way that keeps the solution set.
1
Make the idea visible.
Predict a change, adjust one value, then explain what stayed the same.
Both sides must remain equal. This model builds an equation from a chosen solution; it illustrates the reasoning, rather than testing you.
Keep the solution set unchanged
Add or subtract the same quantity on both sides. Multiply or divide both sides by the same non-zero number. These operations preserve the solutions. Dividing by zero is undefined. With a two-step equation, undo the added constant before undoing multiplication; this follows the structure of the expression.
Show why each step is valid
For 3x + 5 = 20, subtract 5 from both sides: 3x = 15. Divide both sides by 3: x = 5. “Move the 5 and change its sign” is shorthand that hides the operation. Naming what happens to both sides makes the reasoning easier to check, especially with negatives.
Substitute into the original equation
Check x = 5 in the original statement: 3(5) + 5 = 20. The left side gives 20 and the right side is 20, so the solution works. A check in a mistakenly changed equation can miss an earlier error. Keep the original equation available.
Khan Academy
Watch with a purpose
Solving linear equations
Pause before each operation. Identify what must happen to both sides, then compare the reasoning with your own solution.
Watch on YouTube →Use captions when available. The lesson’s explanations and worked examples cover the idea in text.Worked examples
Follow the reasoning.
Solve −3x + 2 = 14
- Subtract 2 from both sides: −3x = 12.
- Divide by −3: x = −4.
- Check: −3(−4) + 2 = 12 + 2 = 14.
Try it with support
Show your thinking.
Solve 5x + 4 = 19 and explain your steps.
Give me a hint
Undo +4 first, then multiplication by 5.
Compare a worked response
x = 3
Subtract 4 from both sides to obtain 5x = 15, then divide by 5.
A student changes 2x + 6 = 14 into 2x = 14. What is missing?
Give me a hint
What happened to the right side?
Compare a worked response
Subtract 6 on both sides.
The valid next equation is 2x = 8. Removing 6 on only one side breaks equality.
Independent practice
Check your understanding.
Fresh questions · useful feedback
Build fluency, one decision at a time.
Work through eight questions. Two independent correct answers introduce a harder version; supported answers bring the next question back to the foundation. You can use hints at any time.
0 of 8 questions completed
This round saves on this device. It is practice, not a school mark.
Check the concepts, too.
Choose a response, then use the explanation to check your reasoning. This is practice, not a school mark.
Go further
Keep the connections close.
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