Algebra

Linear Inequalities

Two-sided Linear Inequalities

         

What is the greatest integer value of xx that satisfies the inequality 52x3<3?-5 \leq 2x - 3 < 3?

Solve the simultaneous inequalities

3x+412x5<5x+1. \begin{aligned} -3x + 4 &\ge 1 \\ 2x - 5 &< 5x + 1. \end{aligned}

Solve the inequalities x23<x+54<x12. \dfrac{x-2}{3} < \dfrac{x+5}{4} < \dfrac{x-1}{2}.

The minimum value of xx that satisfies the inequality x511x43 \dfrac{x - 5}{11 x - 4} \geq 3 can be expressed as ab \dfrac{a}{b} , where aa and bb are coprime positive integers. What is the value of ab? \dfrac{a}{b}?

If the range of xx represented by the arrows in the number line above is equivalent to xa<x1x+b, x - a < -x - 1 \le x + b, what is a+b? a + b ?

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