Chapter EP, Problem 2.8.20EP

To determine

Graph the inequality.

Answer to Problem 2.8.20EP

The graph of inequality $y\ge \left|2x-1\right|+5$

Explanation of Solution

Given information:

The equation $y\ge \left|2x-1\right|+5$ .

Formula used:

First the line of boundary of required region is plotted by putting equals to sign instead of inequality sign. Then the required region is determined by putting a known point in inequality, if the point satisfies the inequality it is region lies on same point as of point, and if the point doesn’t satisfy the inequality region lies on other side of line.

  $\begin{array}{l}y\ge \left|2x-1\right|+5\\ y-\left|2x-1\right|-5\ge 0\end{array}$

Putting equals to sign instead of inequality sign and plotting the line

  $y-\left|2x-1\right|-5=0$

The graph of line $y-\left|2x-1\right|-5=0$

Putting $\left(0,0\right)$ in inequality to determine the region.

  $\begin{array}{l}y\ge \left|2x-1\right|+5\\ 0\ge \left|2\left(0\right)-1\right|+5\\ 0\ge \left|-1\right|+5\\ 0\ge 1+5\end{array}$

  $0\ge 6$

As $\left(0,0\right)$ does not satisfies the inequality, the required region lies on opposite side as of $\left(0,0\right)$ ,

The graph of inequality $y\ge \left|2x-1\right|+5$