Question

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

$-2+3x\ge \frac{1}{3}$

Short answer

Therefore$\frac{5}{6},1,\sqrt{5},3,$ and satisfy the inequality.

Step-by-step solution

Step-1. Consider the inequality.

The objective is to check which elements of the set$S=\left\{-5,1,0,\frac{2}{3},\frac{5}{6},1,\sqrt{5},3,5\right\}$ satisfy the inequality $-2+3x\ge \frac{1}{3}$.

Step-2. Solve the given inequality.

$\begin{array}{c}-2+3x\ge \frac{1}{3}\\ -2+3x\ge \frac{1}{3}+2\\ 3x\ge \frac{7}{3}\end{array}$

Step-3. Apply division on both sides.

$\begin{array}{c}\frac{3x}{3}\ge \frac{7}{9}\\ x\ge \frac{7}{9}\end{array}$

Since,$\frac{5}{6},1,\sqrt{5},3,5,>\frac{7}{9}.$

So,$\frac{5}{6},1,\sqrt{5},$ and$3,5,$ satisfy the inequality.