Question

Graph the solution to the inequality on the numberline |y-3|<8

Answer 1

Let's solve for the possible values of y on the given inequality. It has an absolute value sign, hence, we consider the positive and negative equivalent of the expression on the left-hand side. If we consider the positive value of the expression, we have

`\begin{gathered} y-3<8 \\ y<11 \end{gathered}`

For the negative value, we have

`\begin{gathered} -(y-3)<8 \\ -y+3<8 \\ -y<5 \\ y>-5 \end{gathered}`

The solutions are now provided above. The representation of these solutions on the number line is drawn as