Linear Inequality in One Variable - SS2 Mathematics Past Questions and Answers - page 1
Solve the inequalities below:
\(\frac{x}{2} - 2 \geq \frac{2x}{5} + \frac{1}{4}\)
Multiply each by the LCM of the denominators \(2,\ 5,\ 4 = 20\)
\(10x - 40 \geq 8x + 5\)
\[10x - 8x \geq 40 + 5\]
\[2x \geq 45\]
\(x \geq \frac{45}{2}\)
Users' Answers & CommentsSolve the inequalities below:
\(5(x + 1) \leq 4x + 1\)
\[5(x + 1) \leq 4x + 1\]
\[5x + 5 \leq 4x + 1\]
\[5x - 4x \leq 1 - 5\]
\(x \leq - 4\)
Users' Answers & Comments\(\frac{x - 1}{2} - \frac{x}{3} \nless - \frac{1}{2}\ (Hint:\ \nless is\ \geq )\)
\[\frac{x - 1}{2} - \frac{x}{3} \nless - \frac{1}{2}\]
\[\frac{x - 1}{2} - \frac{x}{3} \geq - \frac{1}{2}\]
\[3(x - 1) - 2x \geq - 3\]
\[3x - 3 - 2x \geq - 3\]
\[x - 3 \geq - 3\]
\[x \geq - 3 + 3\]
\[x \geq 0\]
Users' Answers & Comments\(x \leq 4x + 15\)
\[x \leq 4x + 15\]
\[x - 4x \leq 15\]
\[- 3x \leq 15\]
\[x \geq \frac{15}{- 3}\]
\[x \geq - 5\]
Users' Answers & Comments\(\frac{3x - 1}{x + 2} > 2\)
\[\frac{3x - 1}{x + 2} - 2 > 0\]
\[3x - 1 - (x + 2) > 0\]
\[3x - 1 - x - 2 > 0\]
\[2x - 3 > 0\]
\[2x > 3\]
\[x > \frac{3}{2}\]
Users' Answers & Comments