Question

Solve and check |2x − 1| = |4x + 9|

Answer 1

Answer:

x = -5 or x = -4/3

Step-by-step 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

Answer 2

Answer:

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

this equation can be separated into 2 possible cases :

$2x - 1 = 4x + 9$

and

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

solve the 1st possible case:

$2x - 1 = 4x + 9$

$2x - 4x = 9 + 1$

$- 2x = 10$

$x = - \frac{10}{2}$

$x = - 5$

solve the 2nd possible case:

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

$2x - 1 = - 4x - 9$

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

$6x = - 8$

$x = \frac{ - 8}{6}$

$x = - \frac{4}{3}$

so the x value for this equation is:

x = -5 or x = -1.333