Algebra / Linear Inequalities
Linear Inequalities
Linear inequalities use symbols such as $<$, $>$, $\le$, and $\ge$ to describe ranges of values. Supplemental practice should emphasize integer boundary questions, compound inequalities, strict versus inclusive endpoints, context constraints, and parameter values that determine a solution set.
Least you need to know
- Multiplying or dividing both sides of an inequality by a negative number reverses the inequality symbol.
- Strict inequalities do not include the endpoint, while $\le$ and $\ge$ do.
- Integer-solution questions require translating the final interval into actual integer values.
Key notation
- $x<5$ — All values of $x$ less than 5
- $-2<x\le 7$ — All values greater than -2 and less than or equal to 7
Worked example
- Consider $-3x+5<20$.
- Subtract 5 from both sides: $-3x<15$.
- Divide by $-3$ and reverse the inequality: $x>-5$.
- If the question asks for the least integer solution, the answer is $-4$.
Common mistakes
- Reverse the inequality symbol only when multiplying or dividing by a negative number.
- For integer counts, list or carefully count the integers in the interval.
- A boundary point may fail a strict inequality even if it lies on the boundary line.
How to recognize it
- The problem asks for a least or greatest integer value.
- The problem gives a compound inequality or a real-world maximum/minimum constraint.
- The problem asks which ordered pair satisfies a two-variable inequality.
اگلا تجویز کردہ سبق
اس موضوع کو Linear Inequality Constraints from Contexts کے ساتھ جاری رکھیں۔
Linear Inequality Constraints from Contextsمتعلقہ اسباق
اسی موضوع کے قریبی اسباق کے ساتھ جاری رکھیں۔