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.
الدرس المقترح التالي
تابع هذا الموضوع مع Inequality sign reversal.
Inequality sign reversalدروس ذات صلة
تابع مع دروس قريبة في الموضوع نفسه.