Q29. - Algebra 2

Question

Graph each inequality.

$\left|x+y\right|>1$.

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 $\left|x+y\right|>1$.

The boundary line equaton is $\left|x+y\right|=1$.

Here the inequality is $>$, graph the boundary line as a dashed line.

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

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

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

$\begin{array}{l}\left|x+y\right|>1\\ \left|0+0\right|>1\text{\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}substitute 0 for }x,0\text{ for }y\\ 0>1\text{\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}false}\end{array}$

Step 3 – Conclusion

Since, $0>1$results a false inequality, so, shade the region that does not contains the point $\left(0,0\right).$

Graphical representation of $\left|x+y\right|>1$: