Question

for all numbers x,|x+3|=|x|+3
find the number that provides a counterexample to show that the statement is false
with solution please

Answer 1

Given : for all numbers x,|x+3|=|x|+3

To Find : with an example  show that the statement is false

Solution:

| x + 3 |  = | x |  +  3

x = - 1

=> | x + 3 | = | - 1 + 3 |  = | 2 |  = 2

| x |  + 3 = | - 1 |  + 3  = 1 + 3 = 4

2 ≠ 4

Hence

| x + 3 | ≠ | x |  +  3   for all x

another example

x = - 2

=> | x + 3 | = | -2 + 3 |  = | 1 |  = 1

| x |  + 3 = | - 2 |  + 3  =2 + 3 = 5

1 ≠ 5

Hence

| x + 3 | ≠ | x |  +  3   for all x

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