Your learning journey
Solve linear equations while preserving equality. Check solutions in the original equation, including unknowns on both sides.
Work without a calculator except for an invited check. Keyboard - means the same as −. Attempt before opening a scaffold or intentional practice explanation.
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Ready.
Connect & Check
Solution: value making an equation true. Inverse: operation that undoes another. Balance: both sides represent equal values. Linear: unknown occurs to power one after simplification.
Intentional practice feedback after your attempt
5x.
Collect like terms.
Intentional practice feedback after your attempt
2x+6.
Distribute to both terms.
Intentional practice feedback after your attempt
10.
Substitution checks a proposed solution.
Present
Equality is preserved when the same amount is added to or subtracted from both sides. Multiplying or dividing both sides by the same non-zero number also preserves equality. Undo operations in reverse order; moving terms is shorthand for these balanced operations.
Simplify brackets first. Subtract an unknown term from both sides if needed. Undo addition or subtraction, then multiplication or division. Substitute into the original equation and compare both sides.
Optional scaffold
What undoes subtracting 4?
Intentional practice feedback after your attempt
x=13.
Add 4 on both sides.
Optional scaffold
Reverse the operation order.
Intentional practice feedback after your attempt
x=5.
Add 3 then divide by 4.
Optional scaffold
Or expand correctly first.
Intentional practice feedback after your attempt
x=7.
Divide by 3 then add 2.
Optional scaffold
Put unknown terms on one side.
Intentional practice feedback after your attempt
x=5.
Subtract 4x, add 2, divide by 3.
Apply
Optional scaffold
Write the balanced operation each time.
Intentional practice feedback after your attempt
x=4; x=7; x=−4.
Signs and order change the operations.
Intentional practice feedback after your attempt
x=5; both sides equal 28.
4x+8=3x+13.
Optional scaffold
Let x be the number.
Intentional practice feedback after your attempt
3x+7=31; x=8.
Subtract 7, then divide by 3.
Optional check after A2: enter 4×(5+2) and 3×5+13. Both give 28. Checking does not replace showing the balanced solving steps.
Apply and extend
Intentional practice feedback after your attempt
Dividing by 2 must divide every term: x+3=7, so x=4.
Check 2×4+6=14.
Intentional practice feedback after your attempt
First: all real x. Second: none, since 6 cannot equal 7.
Simplification can remove the unknown; interpret the remaining statement.
Access, Scaffold, Core and Stretch support the same goal. Stretch deepens reasoning for either qualification tier.
Recall & Review
Retrieval without notes
Six retrieval points. Enter a number, decimal, fraction such as 3/2, or mixed number such as 1 1/2. Equivalent numeric values are accepted. Unsupported notation goes to teacher review. For rounding, also communicate the requested accuracy in written work; numerical scoring cannot judge significant trailing zeros.
Not checked.
Independent exit evidence
P1–P2: five minutes, no notes, 4 marks. Your teacher reviews working and explanations. Full assessment solutions are not embedded.
Recall & Review and prepare
Translate the situation before solving. Define the unknown and its units, form the equation, solve it, then decide whether the answer makes sense in the context.
Retrieve F1 again in one week. Bring your working and one question.
Your progress summary
Completion records attempts, not mastery. Retrieval points describe the latest checked attempt. Your teacher reviews P1–P2 separately and checks retained understanding after a delay.
Restore a backup
Original Reach for the Star. Not an official or endorsed Pearson resource. Separate teacher package contains assessment solutions. Local saving is browser-dependent; no account or dashboard service is included.
Optional extension activities
Allow 10–15 minutes if the main practice is secure. Show your method, explain a check and justify your conclusion.
Stretch
Reveal a worked check after attempting
10x−5=3x+16, so 7x=21, x=3; both sides 25.
Deep challenge
Reveal a worked check after attempting
Divide every term: x+2=4, so x=2.