Question

Solve the equation |x-2|-3=0 first by finding the zeros of
y=|x-2|-3 and then algebraically.

Answer 1

The solution of given equation are -1 and 5.

Explanation:

The given equation is

`|x-2|-3=0`

We need to solve the above equation by finding the zeros of

`y=|x-2|-3`

The vertex form of an absolute function is

`y=a|x-h|+k`

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.

`|x-2|-3=0`

Add 3 on both sides.

`|x-2|=3`

`x-2=\pm 3`

Add 2 on both sides.

`x=\pm 3+2`

`x=3+2` and
`x=-3+2`

`x=5` and
`x=-1`

Therefore the solution of given equation are -1 and 5.