Question

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

$1-2x\ge 5x$

Short answer

The element from the given set that satisfies the given inequality are $\left\{-5,-1,0\right\}.$

Step-by-step solution

Step-1. Consider the inequality.

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

Step-2. Solve the given inequality.

$1-2x\ge 5x$

$1-2x+2x\ge 5x+2x$ (Add on both sides).

Step-3. Apply division into the obtained equation.

$\begin{array}{c}\frac{1}{7}\ge \frac{7x}{7}\\ \frac{1}{7}\ge x\end{array}$

Thus, implies that must be less than $\frac{1}{7}$. So, the elements satisfies the given inequality are$\left\{-5,-1,0\right\}.$