Solve the following system of equations in R.
2x−7>5−x,11−5x≤1
Consider the first inequation,
2x−7>5−x⇒2x+x>5+7⇒3x>12⇒x>123⇒x>4 ...(i)Consider the second inequation,11−5x≤1⇒−5x≤1−11⇒−5x≤−10⇒5x≥10⇒x≥2 ...(ii)From (i) and (ii),(4,∞)is the solution set of the simultaneous equations.