Question

Solve and check |2x − 1| = |4x + 9|

Answer 1

`|2x - 1| = |4x + 9|`

this equation can be separated into 2 possible cases :

`2x - 1 = 4x + 9`

and

`2x - 1 = - (4x + 9)`

solve the 1st possible case:

`2x - 1 = 4x + 9`

`2x - 4x = 9 + 1`

`- 2x = 10`

`x = - (10)/(2)`

`x = - 5`

solve the 2nd possible case:

`2x - 1 = - (4x + 9)`

`2x - 1 = - 4x - 9`

`2x + 4x = - 9 + 1`

`6x = - 8`

`x = ( - 8)/(6)`

`x = - (4)/(3)`

so the x value for this equation is:

x = -5 or x = -1.333

Answer 2

x = -5 or x = -4/3

Explanation:

First possibility.

|2x − 1| = |4x + 9|

2x - 1 = 4x + 9

2x - 4x = 9 + 1

-2x = 10

x = 10/-2

x = -5

Second possibility.

2x - 1 = - (4x+9)

2x - 1 = -4x - 9

2x + 4x = -9 + 1

6x = -8

x = -8/6

x = -4/3