Question

options how many possible solutions

1,
2,
3,
4,

Answer 1

Topic

Modulus Function

Given

| | 2x - 3 | - m | = m

where

m > 0

To Find

Number of solution does given equation have.

Solution

| | 2x - 3 | - m | = m

| 2x - 3 | - m = ± m

| 2x - 3 | = m ± m

| 2x - 3 | = 2m, 0

Now, take cases,

Case 1

| 2x - 3 | = 2m

2x - 3 = ± 2m

2x = 3 ± 2m

x = ( 3 ± 2m ) / 2

x = ( 3 + 2m ) / 2 , ( 3 - 2m ) / 2

We get two values of 'x' from this case.

Case 2

| 2x - 3 | = 0

2x - 3 = 0

x = 3/2

So, we get one value from this case.

Answer

So, there are 3 solutions of the given equation.

Additional Information

Properties of Modulus

| a | ≥ 0

| a | = | -a |

|ab| = | a || b |

√a² = | a |