Solve x/5 = −4
- Multiply both sides by 5.
- x = 5(−4) = −20.
- Check: (−20)/5 = −4.
Equations with division
Undo division by multiplying—and keep the whole equation balanced.
Lesson 04 · Start where you need
Your learning goal
Solve x ÷ a = b and x ÷ a + b = c, with a non-zero divisor, and verify the result.
Read the fraction bar as division
The expression x/3 means x divided by 3. It does not mean 3x. In x/3 = 5, three equal shares each have value 5, so the original total x is 15. Multiplying both sides by 3 preserves equality: 3(x/3) = 3(5).
Words worth knowing
- Divisor
- The non-zero number by which a quantity is divided.
- Inverse operation
- Multiplication undoes division by the same non-zero number.
- Solution
- A value that makes the original equation true.
1
Make the idea visible.
Predict a change, adjust one value, then explain what stayed the same.
Read x ÷ a as division. Multiplying both sides by the non-zero divisor a preserves equality and isolates x after the constant is removed.
Undo operations in reverse order
In x/4 + 2 = 7, x is first divided by 4 and then increased by 2. Subtract 2 from both sides to get x/4 = 5. Multiply both sides by 4 to obtain x = 20. Check in the original equation: 20/4 + 2 = 5 + 2 = 7.
Negative divisors still need equal operations
For x/(−3) + 4 = 9, subtract 4 from both sides: x/(−3) = 5. Multiply both sides by −3 to get x = −15. A negative divisor changes the sign of the product; it does not change the principle of equality. Check: (−15)/(−3) + 4 = 9.
Brackets change what is divided
Compare x/3 + 2 with (x + 2)/3. In the first, only x is divided by 3; in the second, the entire sum x + 2 is divided by 3. At x = 6 the first equals 4 and the second equals 8/3. Read the grouping before deciding which inverse operation to use. A divisor of zero is never permitted.
Worked examples
Follow the reasoning.
Solve x/(−2) − 3 = 5
- Add 3 to both sides: x/(−2) = 8.
- Multiply both sides by −2: x = −16.
- Check: (−16)/(−2) − 3 = 8 − 3 = 5.
Try it with support
Show your thinking.
Solve x/6 + 4 = 2.
Give me a hint
Undo the added 4 first.
Compare a worked response
x = −12
Subtract 4 to get x/6 = −2; multiply by 6. Check: −12/6 + 4 = 2.
A student turns x/4 = 3 into x = 3/4. Explain the error.
Give me a hint
Which operation undoes dividing by 4?
Compare a worked response
Multiply both sides by 4.
x = 12. Dividing by 4 again does not undo the original division.
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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