Linear Inequality in One Variable - SS2 Mathematics Past Questions and Answers - page 1

Multiply each by the LCM of the denominators \(2,\ 5,\ 4 = 20\)

\(10x - 40 \geq 8x + 5\)

\[10x - 8x \geq 40 + 5\]

\[2x \geq 45\]

\(x \geq \frac{45}{2}\)

\[5(x + 1) \leq 4x + 1\]

\[5x + 5 \leq 4x + 1\]

\[5x - 4x \leq 1 - 5\]

\(x \leq - 4\)

\[\frac{x - 1}{2} - \frac{x}{3} \nless - \frac{1}{2}\]

\[\frac{x - 1}{2} - \frac{x}{3} \geq - \frac{1}{2}\]

\[3(x - 1) - 2x \geq - 3\]

\[3x - 3 - 2x \geq - 3\]

\[x - 3 \geq - 3\]

\[x \geq - 3 + 3\]

\[x \geq 0\]

\[x \leq 4x + 15\]

\[x - 4x \leq 15\]

\[- 3x \leq 15\]

\[x \geq \frac{15}{- 3}\]

\[x \geq - 5\]

\[\frac{3x - 1}{x + 2} - 2 > 0\]

\[3x - 1 - (x + 2) > 0\]

\[3x - 1 - x - 2 > 0\]

\[2x - 3 > 0\]

\[2x > 3\]

\[x > \frac{3}{2}\]