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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

Two-sided Linear Inequalities

What is the greatest integer value of $x$ that satisfies the inequality $-5 \leq 2x - 3 < 3?$

4 3 2 1

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by Brilliant Staff

Solve the simultaneous inequalities

$\begin{aligned} -3x + 4 &\ge 1 \\ 2x - 5 &< 5x + 1. \end{aligned}$

-1 < x \le 2

-2 < x \le 1

-2 \le x < 1

-1 \le x < 2

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by Brilliant Staff

Solve the inequalities $\dfrac{x-2}{3} < \dfrac{x+5}{4} < \dfrac{x-1}{2}.$

-7 < x < 7

3 < x < 7

7 < x < 23

3 < x < 23

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by Brilliant Staff

The minimum value of $x$ that satisfies the inequality $\dfrac{x - 5}{11 x - 4} \geq 3$ can be expressed as $\dfrac{a}{b}$ , where $a$ and $b$ are coprime positive integers. What is the value of $\dfrac{a}{b}?$

\dfrac{1}{4}

\dfrac{7}{32}

\dfrac{4}{11}

\dfrac{2}{5}

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If the range of $x$ represented by the arrows in the number line above is equivalent to $x - a < -x - 1 \le x + b,$ what is $a + b ?$

4 8 10 12

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by Brilliant Staff

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