Q30. - Algebra 2

Question

Graph each inequality.

$\left|x\right|\le \left|y\right|$.

Step-by-Step Solution

Answer

The graph of the inequality is shown below:

Step 1 – Find the boundary line equation of the given equation.

Consider the inequality $\left|x\right|\le \left|y\right|$.

The boundary line equaton is $\left|x\right|=\left|y\right|$.

Here the inequality is $\le$, graph the boundary line as a solid line.

Step 2 – Choose a test point and test the inequality.

Choose the test point as $\left(0,1\right).$

Substitute $x=0,y=1$in $\left|x\right|\le \left|y\right|$:

$\begin{array}{l}\left|x\right|\le \left|y\right|\\ \left|0\right|\le \left|1\right|\text{\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}substitute 0 for }x,1\text{ for }y\\ 0<1\text{\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}true}\end{array}$

Choose another test point as $\left(0,-1\right).$

Substitute $x=0,y=-1$in $\left|x\right|\le \left|y\right|$:

$\begin{array}{l}\left|x\right|\le \left|y\right|\\ \left|0\right|\le \left|-1\right|\text{\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}substitute 0 for }x,-1\text{ for }y\\ 0<1\text{\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}true}\end{array}$

Step 3 &ndash; Conclusion

Since, $0<1$results a true inequality, so, shade the region that contains the points$\left(0,1\right),\left(0,-1\right).$

Graphical representation of $\left|x\right|\le \left|y\right|$