How do I solve the equation |4x+6|=5

Question

Solve the equation

 

Answer 1

Hi Arie;

|4x+6|=5

Because this is absolute value...

+(4x+6) is the same as -(4x+6).

4x+6=5............-(4x+6)=5

4x=-1...............-4x-6=5

x=-1/4...............-4x=11

.........................x=-11/4

 

Let's check our results...

|4x+6|=5

x=-1/4

|[(4)(-1/4)]+6|=5

|-1+6|=5

5=5

 

x=-11/4

|[(4)(-11/4)]+6|=5

|-11+6|=5

|-5|=5

5=5

 

 

 

Answer 2

Arie,

            An absolute value question requires two answers because 2 numbers will have the same absolute value. For instance, both 5 and -5 have an absolute value of 5.

 

So the 2 equations you use are 4x + 6 =5 and 4x +6 = -5

 

4x + 6 =5  4x = -1  x = -1/4

 

4x + 6 = -5  4x = -11  x = -11/4

 

Hope this helps