Q27. - Algebra 2

Question

Graph each inequality.

27. $y+\left|x\right|<3$.

Step-by-Step Solution

Answer

The graph of the inequality is shown below:

Step 1 &ndash; Find the boundary line equation of the given equation.

Consider the inequality $y+\left|x\right|<3$.

The boundary line equaton is $y+\left|x\right|=3$.

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

Step 2 &ndash; Choose a test point and test the inequality.

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

Substitute $x=0,y=0$in $y+\left|x\right|<3$:

$\begin{array}{l}y+\left|x\right|<3\\ 0+\left|0\right|<3\text{\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}substitute 0 for }x,0\text{ for }y\\ 0<3\text{\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}true}\end{array}$

Step 3 &ndash; Conclusion

Since, $0<3$results a true inequality, so, shade the region that contains the point $\left(0,0\right).$

Graphical representation of $y+\left|x\right|<3$: