Which one of the following is a representation (not to scale and in bold) of all values of x satisfying the inequality 2 - 5x >= -(6x - 3)/3 on the real number line? A. <--- [closed dot] x=1 ------> B. <--- ------- [open dot] x=1 ---> C. <--- [closed dot at -1] x=-1 ------> D. <--- ------- [open dot at -1] x=-1 ->

GATE 2022 · General Aptitude · Inequality · medium

Answer: x <= 1/3. The correct number line is option C: closed dot at 1/3 with bold shading to the left.

1. Clear the fraction — multiply both sides by 3: 6 - 15x >= -6x + 3
2. Collect x-terms on the right and constants on the left: 3 >= 9x => x <= 3/9 => x <= 1/3
3. Identify the number line representation: The solution is all x up to and including 1/3: closed (filled) dot at 1/3, bold arrow going left toward -infinity. This matches option C in the question.