Two-sided Linear Inequalities Practice Problems Online

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

Solve the simultaneous inequalities

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

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

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 $\dfrac{a}{b}?$

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 $a + b ?$

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Two-sided Linear Inequalities