Question

Solution? Let $S=\left\{-5,-1,0,\frac{2}{3},\frac{5}{6},1,\sqrt{5},3,5\right\}.$ Determine which elements of satisfying the inequality.

$1<2x-4\le 7$

Short answer

The solution set is or$\left\{x:x>2.5\right.$or$\left.x\le 5.5\right\}=\left\{3,5\right\}.$

Step-by-step solution

Step-1. Consider the inequality.

The given inequality is $1<2x-4\le 7$.

Step-2. Separate the given inequality.

So, we have $1<2x-4$or$2x-4\le 7.$

Step-3. Simplify the two obtained equations.

$5<2x$ Or $x\le \frac{11}{2}$

$x>\frac{5}{2}$ Or $x\le 5.5$

$x>2.5$

So, the solution set is $\left\{x:x>2.5\right.$or$\left.x\le 5.5\right\}=\left\{3,5\right\}.$