Answer:
The solution of given equation are -1 and 5.
Step-by-step explanation:
The given equation is
[tex]|x-2|-3=0[/tex]
We need to solve the above equation by finding the zeros of
[tex]y=|x-2|-3[/tex]
The vertex form of an absolute function is
[tex]y=a|x-h|+k[/tex]
where, a is constant and (h,k) is vertex.
Here, h=2, k=-3. So vertex of the function is (2,-3).
The table of values is
x y
0 -1
2 -3
4 -1
Plot these points on a coordinate plane and draw a V-shaped curve with vertex at (2,-3).
From the given graph it is clear that the graph intersect x-axis at -1 and 5. So, zeroes of the function y=|x-2|-3 are -1 and 5.
Therefore the solution of given equation are -1 and 5.
Now solve the given equation algebraically.
[tex]|x-2|-3=0[/tex]
Add 3 on both sides.
[tex]|x-2|=3[/tex]
[tex]x-2=\pm 3[/tex]
Add 2 on both sides.
[tex]x=\pm 3+2[/tex]
[tex]x=3+2[/tex] and [tex]x=-3+2[/tex]
[tex]x=5[/tex] and [tex]x=-1[/tex]
Therefore the solution of given equation are -1 and 5.
