An equation states that two expressions have the same value. Solving it means preserving that equality while isolating the unknown. Think of doing the same operation to both sides instead of memorising that a term ‘jumps across’ and changes sign.
Original foundation practice · choose by prerequisite skill.
PREDICT · CHANGE · EXPLAIN
The expression y=3x+2 equals 17 only at one x-value. Predict x, move the slider, then verify it by substitution.
The curve shows this simplified model over the labelled range. Read the exact point below; the sketch is not a measuring instrument.
3x + 2: 8
Which x makes the output 17? Explain the operations that lead there.
Now close the explanation and try the independent retest. Moving a slider alone does not check your understanding.
Start here if moving terms changes signs unpredictably or brackets cause errors. This lesson repairs the one-unknown step before simultaneous or quadratic equations; it does not duplicate the Class 10 two-variable modelling lesson.
Solve x + 4 = 9. Name the operation on both sides and substitute your answer into the original equation.
You will need: Signed arithmetic and the distributive law.
Attempt each task before opening a hint. If you need help, reveal the first hint, then the setup, then compare your written steps with the solution. Finish with the retests without referring back.
Adding or subtracting the same quantity on both sides preserves equality. Multiplication or division by the same non-zero number also preserves it.
Expand a bracket by multiplying every term inside it. In 3(x−2), the constant contribution is −6.
An equation may have one solution, no solution or every value as a solution. After simplification, a false statement signals none and an identity signals all allowed values.
Undo the addition before undoing multiplication.
Subtract 2 from both sides to get 3x=15.
Both sides lose 2.
x=5 and 3(5)+2=17.
Answer: x=5
Before moving on: can you explain why your method works, as well as give the answer?
Write a method as well as an answer. The tasks change the reasoning, not just the numbers.
You can divide both sides by 2 first.
x−3=5.
The full left side is halved.
Add 3 to both sides: x=8.
Answer: x=8
Before moving on: can you explain why your method works, as well as give the answer?
Gather the x terms on one side.
Subtract 2x, then add 4.
3x−4=11, then 3x=15.
x=5; each original side is 21.
Answer: x=5
Before moving on: can you explain why your method works, as well as give the answer?
Expand the bracket.
Subtract 2x from both sides.
2x+2=2x+5.
The remaining statement 2=5 is false for every x.
Answer: No solution
Before moving on: can you explain why your method works, as well as give the answer?
A tempting claim: “A term changes sign simply because it crosses the equals sign.”
The shortcut hides the operation preserving equality and breaks down with brackets or division.
These changed questions test whether you can reconstruct the method. If you use a hint, record where you got stuck and retry later. Completing this small set does not establish full chapter mastery.
Undo +3, then ×4.
4x=24.
27−3=24.
x=6; 4(6)+3=27.
Answer: x=6
Could you solve this without the earlier example? If not, revisit the first line where you got stuck.
Expand the left side.
Both sides become identical.
3x+6=3x+6.
This holds for every real x.
Answer: Every real x
Could you solve this without the earlier example? If not, revisit the first line where you got stuck.
Try the two retests with examples closed. If the same error returns, correct that step and retry later; this short practice is not a diagnostic score or a grade assessment.
Ask the learner to say the operation at each line and check the original equation. Do not treat a correct result from unexplained sign-changing as proof that the difficulty is resolved.
If the retests are independent, return to the problem that brought you here. The linked Class 10 application is optional for learners already studying that topic; younger learners should use their current school exercise.
Only if you know it is non-zero for the case being considered. Dividing by an expression that may be zero can lose valid solutions.
Yes. Use the two print buttons above. The question sheet leaves working space and hides solutions; the worked-solutions option includes the solution steps. Your browser can save either view as a PDF.
PERSONAL SUPPORT
Bring one attempted question and the step that caused difficulty. Discuss suitable TutorMax support for the learner's current level.
Discuss the right Maths starting point