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PolarNik [594]
3 years ago
12

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

Mathematics
1 answer:
tino4ka555 [31]3 years ago
3 0

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.

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