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Algebra

Linear Inequalities

Concept Quizzes

Linear Inequalities Warmup
Finding Solutions to Linear Inequalities
Inequalities - Solution Set
One-Step Linear Inequalities
Multi-Step Linear Inequalities
Two-sided Linear Inequalities
Absolute Value Linear Inequalities
Linear Inequalities Word Problems
Linear Inequalities - Problem Solving

Challenge Quizzes

Linear Inequalities: Level 1 Challenges
Linear Inequalities: Level 2 Challenges
Linear Inequalities: Level 3 Challenges

Linear Inequalities - Problem Solving

If $x+y = 7$ and $4 \leq x \leq 19,$ what is the range of $y?$

{-11} \leq y \leq {4}

{-14} \leq y \leq {1}

{-13} \leq y \leq {2}

{-12} \leq y \leq {3}

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by Brilliant Staff

If the inequality $a^2(x+1)>576 x+24a$ holds for all real numbers $x,$ what is the constant $a?$

24 576 -24 -576

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by Brilliant Staff

Let $x>\frac{14}{13}$ be the solution to the inequality $bx-(a+b)<0,$ where $a$ and $b$ are constants. Then what is the solution to the inequality $ax+2a+b<0?$

x>-15

x<-15

x<15

x>15

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by Brilliant Staff

A factory produces two products $A$ and $B$ using raw materials $p$ and $q$ . It uses $3$ units of $p$ and $1$ unit of $q$ to produce one unit of $A$ . It uses $1$ unit of $p$ and $2$ units of $q$ to produce one unit of $B$ . The maximum daily supplies are $30$ units of $p$ and $20$ units of $q.$ If the profit per unit of $A$ is $\$3$ and the profit per unit of $B$ is $\$2$ , what is the maximum total daily profit (in dollars)?

36 42 33 27

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by Brilliant Staff

Real numbers $x$ and $y$ satisfy $-3 < x < 1$ and $-1 < y < 5$ . What is the range of $x - y ?$

-4 < x-y < 6

-4 < x-y < -2

2 < x-y < 4

-8 < x-y < 2

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by Brilliant Staff