Question

The number of values of x satisfying $3x-3\le 7x+5and5-x\ge \left(\frac{x}{4}\right)-\left(\frac{5}{4}\right),xϵN.$ is .

• A. 4
• B. 5
• C. 7
• D. 6

Answer 1

The correct option is B 5

We have,
$3x-3\le 7x+5and5-x\ge \left(\frac{x}{4}\right)-\left(\frac{5}{4}\right)\Rightarrow -3-5\le 7x-3xand-x-\left(\frac{x}{4}\right)\ge -\left(\frac{5}{4}\right)-5\Rightarrow -8\le 4xand\left(\frac{-5}{4}\right)x\ge \left(\frac{-25}{4}\right)\Rightarrow -2\le xandx\le \left(\frac{-25}{4}\right)\times \left(\frac{-4}{5}\right)\Rightarrow -2\le xandx\le 5\Rightarrow -2\le x\le 5.$

$But,xϵN,i.e.,xϵ\{1,2,3,4,\mathrm{5......}\}.So,thesolutionsetis\{1,2,3,4,5\}.$

The graph of the solution set is shown by thick dots on the following number line:-