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

Solve the equation

Vivian L. | Microsoft Word/Excel/Outlook, essay composition, math; I LOVE TO TEACHMicrosoft Word/Excel/Outlook, essay comp...
3.0 3.0 (1 lesson ratings) (1)
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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

John L. | Experienced Tutor Specializing in Adult Learners and Test PrepExperienced Tutor Specializing in Adult ...
4.9 4.9 (134 lesson ratings) (134)
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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