Your learning journey
Solve linear inequalities and represent solution sets on number lines. Explain endpoint inclusion and order reversal.
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
Inequality: comparison using <, >, ≤ or ≥. Endpoint: boundary value. Solution set: all allowed values. Strict: excludes equality. Integer: whole number, possibly negative.
Intentional practice feedback after your attempt
−2.
Further right on the number line.
Intentional practice feedback after your attempt
x=4.
Equation boundary method.
Intentional practice feedback after your attempt
3.
Two negative signs give a positive quotient.
Present
Adding the same number preserves order. Multiplying by a negative reverses order: 2<5 becomes −2>−5. A solution such as x≥3 contains many values. The filled endpoint includes 3; an arrow to the right includes larger values.
Solve using balanced operations. Reverse the inequality when multiplying or dividing by a negative number. Mark the endpoint and direction, then test one value inside and one outside the set.
Optional scaffold
Test −1 and 0.
Intentional practice feedback after your attempt
Filled circle at −1; ray to the right.
−1 is included, and all greater values.
Optional scaffold
Addition preserves order.
Intentional practice feedback after your attempt
x≥5.
Add 3 on both sides.
Optional scaffold
The direction stays the same.
Intentional practice feedback after your attempt
x>4.
Add 2, divide by positive 3.
Optional scaffold
Check x=−5 and x=0.
Intentional practice feedback after your attempt
x≤−4.
Division by −3 reverses the sign.
Apply
Optional scaffold
Test the endpoint first.
Intentional practice feedback after your attempt
Open left; filled left; open right; filled right.
Strictness and direction are separate choices.
Intentional practice feedback after your attempt
x≤4; 1,2,3,4.
The integer condition narrows the real solution set.
Optional scaffold
v is a non-negative integer.
Intentional practice feedback after your attempt
5+3v≤20; v≤5; maximum 5 visits.
At most includes equality.
Optional numerical check for −3x≥12: x=−5 gives 15≥12, while x=0 gives 0≥12 false. A calculator tests selected values; it does not describe the full set.
Apply and extend
Intentional practice feedback after your attempt
x=0 fits the original but not the claim. Correct x≥−4.
Division by a negative reverses order.
Intentional practice feedback after your attempt
−1,0,1,2,3.
−2 is excluded; 3 is included.
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
An arithmetic sequence has a constant difference. For 5,8,11,14,... the nth term is 3n+2 when the first term is n=1. Check both the first term and the difference.
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
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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
−2x<8, so x>−4; all numbers greater than −4.
Deep challenge
Reveal a worked check after attempting
x≤−4; multiplying an inequality by a negative reverses order, e.g. −3×−4=12 and x=−5 gives 15≥12.