Q52. - Algebra 2

Question

Graph each inequality.

$52. 2x+y\ge 3$

Step-by-Step Solution

Answer

The graph of inequality is as shown.

Step-1 – convert the given in equation in to equation

$\begin{array}{l}2x+y\ge \mathrm{3.......}\left(1\right)\\ 2x+y=3\end{array}$

Step-2 – Solving for point identification

To solve the equation by putting the value of given variables one by one zero we get,

$\begin{array}{ccc}x& 0& 1.5\\ y& 3& 0\end{array}$

Step-3 – solve to identify the shaded region with respect to origin

Now, substitute point $\left(0,0\right)$ in first equation we get,

$\begin{array}{l}2x+y\ge 3\\ 2\left(0\right)+0\ge 3\\ 0\ge 3\end{array}$

$0\ge 3$ It is not true, so that shaded region fall away from  the origin.

Step-4 – Plot the graph

Hence, the graph of inequality is as shown.