Solve 1/3|2x – 5| = 2 for x. ?

Question

The " | " isn't the same thing as brackets and I dunno how to solve it.

Answer 1

1/3 |2x - 5| = 2

|2x - 5| = 2(3)

|2x - 5| = 6

2x - 5 = +/- 6

2x - 5 = 6

2x = 11

x = 11/2

...OR...

2x - 5 = -6

2x = -1

x = -1/2

(...)<==== this is brackets

|...| <==== this is no a bracket but i forget what it named... i only know what number in |...| will become positive...

Answer 2

" I " means absolute value.

1/3I2x-5I = 2

I2x-5I1/3 = 2

I2x-5I = 6

2x-5 =6

2x = 11

x = 11/2

x = 5.5  

Answer 3

Is the "l" supposed to mean absolute value?

Answer 4

|x| is an absolute value (see source).

so.

1/3. |2x - 5| = 2

|2x - 5| = 6 or -6

|2x| = 11 or -1

x = 5.5 or 0.5

Answer 5

1/3|2x - 5| = 2

|2x - 5| = 2(3/1)

|2x - 5| = 6

2x - 5 = ±6

2x - 5 = 6

2x = 6 + 5

2x = 11

x = 11/2 (5.5)

2x - 5 = -6

2x = -6 + 5

2x = -1

x = -1/2 (-0.5)

∴ x = -1/2 (-0.5) , 11/2 (5.5)  

Answer 6

the " | " sign defines the absolute value and it is defined like this:

|2x – 5| = 2x - 5 if (2x - 5) ≥ 0

or

|2x – 5| = -(2x - 5) if (2x - 5) < 0

=>

|2x – 5| = 2x - 5 if x ≥ 5/2

or

|2x – 5| = -2x + 5 if x < 5/2

Let's consider the first situation:

1. x ≥ 5/2 => |2x – 5| = 2x - 5

the equation becomes:

1/3(2x – 5) = 2 => 2x - 5 = 6 => 2x = 11 => x = 11/2

11/2 > 5/2 =>  x = 11/2 is a valid solution

2. the second case: x < 5/2 => |2x – 5| = -2x + 5

the equation becomes:

1/3(-2x + 5) = 2 => -2x + 5 = 6 => 2x = -1 => x = -1/2

-1/2 < 5/2 so this is also a valid solution

=> the solutions of the equation are:

x = 11/2 = 5 1/2

and

x = -1/2