Question

Select all the values of x that make the equation | 3x + 4 | − 9 = 0 true.

A . 1 2/3
B. -1 2/3
C. 4 1/3
D. -4 1/3
E. 5 2/3
F. -5 2/3

Answer 1

`|3x+4|-9=0`

Add 9 to both sides:

`|3x+4|-9+9=0+9`

`|3x+4|=9`

Solve the Absolute Value:

`3x+4=9or3x+4=-9`

__________________________________________________________

`3x+4=9`

Subtract 4 from both sides:

`3x+4-4=9-4`

`3x=5`

Divide both sides by 3:

`(3x)/(3) =(5)/(3)`

`\fbox{x = $(5)/(3) $ or 1$(2)/(3)$}`

__________________________________________________________

`3x+4=-9`

Subtract 4 from both sides:

`3x+4-4=-9-4`

`3x=-13`

Divide both sides by 3:

`(3x)/(3) =(-13)/(3)`

`\fbox{x = $(13)/(3) $ or -4$(1)/(3) $}`

________________________________________________________

`\fbox{Options A and D}`