Algebra / Linear Inequalities
Inequality Traps and Integer Boundaries
Inequality questions are error-prone because strict versus inclusive endpoints, negative division, compound inequalities, and integer boundaries all affect the final answer.
Least you need to know
- Dividing or multiplying by a negative reverses the inequality sign.
- Strict inequalities do not include the endpoint.
- $\le$ and $\ge$ include the endpoint.
- For integer questions, translate the interval into actual integer values before answering.
Key notation
- $-2<x\le5$ — Values greater than -2 and less than or equal to 5
- $-3x+7<22$ — An inequality that requires reversing the symbol when dividing by -3
Worked example
- Solve $-4x+3\le19$.
- Subtract 3: $-4x\le16$.
- Divide by $-4$ and reverse the inequality: $x\ge -4$.
Common mistakes
- A boundary may satisfy a non-strict inequality but fail a strict inequality.
- The least integer greater than $-3$ is $-2$, not $-3$.
- Context constraints may require a whole number even if the algebraic solution is not an integer.
How to recognize it
- The problem asks for least or greatest integer values.
- The inequality has a negative coefficient on the variable.
- The problem uses phrases such as fewer than, at least, at most, or no more than.
နောက်တစ်ခုပြန်ကြည့်ရန် အကြံပြုထားသော သင်ခန်းစာ
ဤခေါင်းစဉ်ကို Inequality sign reversal ဖြင့် ဆက်လက်သင်ယူပါ။
Inequality sign reversalဆက်စပ်သင်ခန်းစာများ
တူညီသော ခေါင်းစဉ်အတွင်း အနီးစပ်ဆုံး သင်ခန်းစာများနှင့် ဆက်လက်သင်ယူပါ။