Question

Represent the set of real values of x on the number line satisfying $\frac{1}{2}(2x-1)\le 2x+\frac{1}{2}\le 5\frac{1}{2}+x$. Also, find the greatest and the values of x satisfying the inequations.

• A. $x\in [1,5]$
• B. $x\in [-1,5]$
• C. $x\in [-4,3]$
• D. $x\in [4,3]$

Answer 1

Answer: (B)

$x\in [-1,5]$

$Thesystemofequationsis\frac{1}{2}(2x-1)\ge 2x+\frac{1}{2}\ge 5\frac{1}{2}+x.So\frac{1}{2}(2x-1)\ge 2x+\frac{1}{2}⟹2x-1\ge 4x+1⟹2x-4x=1+1⟹x\ge -1.Again2x+\frac{1}{2}\ge 5\frac{1}{2}+x⟹4x+1\ge 11+2x⟹4x-2x\ge 11-1⟹2x\ge 10⟹x\ge 5.\therefore x\in [-1,5].$