Question

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

Answer 1

Answer:

The solution of given equation are -1 and 5.

Step-by-step 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.