Given the below
[tex]|2x-3|-7=0[/tex]
We solve for x as shown below
[tex]\begin{gathered} |2x-3|-7=0 \\ |2x-3|-7+7=0+7 \\ |2x-3|=7 \end{gathered}[/tex]
Let us apply the absolute rule. Absolute rule is as shown below
[tex]|x|=a,a>0,then,x=-a,or,x=a[/tex][tex]\begin{gathered} So,|2x-3|=7,\text{becomes} \\ 2x-3=7,or,2x-3=-7 \\ 2x-3+3=7+3,or,2x-3+3=-7+3 \\ 2x=10,or,2x=-4 \\ \frac{2x}{2}=\frac{10}{2},or,\frac{2x}{2}=\frac{-4}{2} \\ x=5,or,x=-2 \end{gathered}[/tex]
The absolute value of the given equation in set notation is {-2, 5}
