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Linear Inequalities

When is 2x greater than x? Compare algebraic expressions with linear inequalities.

Two-Sided

         

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

Solve the simultaneous inequalities

\[ \begin{align} -3x + 4 &\ge 1 \\ 2x - 5 &< 5x + 1. \end{align} \]

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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