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A linear inequality resembles a linear equation but with an inequality symbol instead of an equals symbol.

For example, $y≤x+5$is a linear inequality with y=x+5 as a related linear equation.

Also, the graph of y=x+5 separates the coordinate plane into two region. The line of the this graph acts as a boundary of the two separated region.

The absolute value function, written as $f\left(x\right)=\left|x\right|$is defined as follows:

For examples, $\left|-2\right|=2;\left|2\right|=2;\left|3.5\right|=3.5;\left|-3.5\right|=3.5$

The given linear equality is $y<4\left|x-1\right|$and thus the boundary which separates the coordinate plane into two region is $y=4\left|x-1\right|$. As the inequality symbol is$<$ and therefore the boundary line will a dotted line which means that the line is not included.

Find the value of y corresponding to the value of x.

Hence by using the values in the table, the graph is obtained as shown below:

Choose a point which is not on a boundary line.

Since the point (0, 0) is not on a boundary line, test the point (0, 0) on the inequality $y<4\left|x-1\right|$.

Therefore,

which is true.

Therefore, shade the region which contain (0, 0).

Hence the graph of the linear inequality is as shown below: