SOLUTION: /3x+2/= 14 / / means absolute value This problem has either 2 solutions or "no solutions"

Question 91996: /3x+2/= 14
/ / means absolute value
This problem has either 2 solutions or "no solutions"
Found 3 solutions by stanbon, homeworkhelpanytime, bucky:
Answer by stanbon(75887)   (Show Source): You can put this solution on YOUR website!
/3x+2/= 14
--------
3x+2 = 14 or 3x+2 = -14
3x = 12 or 3x = -16
x = 4 or x = -16/3
=================
Cheers,
Stan H.
Answer by homeworkhelpanytime(21)   (Show Source): You can put this solution on YOUR website!
|3x+2|= 14
value of |3x+2| is (3x + 2) for x>-2/3
and -3x-2 for x<-2/3
when x>-2/3
3x + 2 = 14
x = 4
when x<-2/3
-3x-2 =14
x =-16/3
Answer by bucky(2189)   (Show Source): You can put this solution on YOUR website!
Given:
.

.
You are to solve for x. A way to do this is to take the quantity inside the absolute
value signs and precede it with plus and minus signs and solve it like an equation.
.
In other words, the quantity inside the absolute value signs is (3x + 2). So you set up two
equations ... one using +(3x+2) and the other using -(3x+2).
.
The first equation is:
.
+(3x +2) = 14
.
Since the parentheses are preceded by a plus sign, you can just remove them to get:
.
3x + 2 = 14
.
Get rid of the 2 on the left side by subtracting 2 from both sides to get:
.
3x = 12
.
Solve for x by dividing both sides by 3 and you get:
.
x = 12/3 = 4
.
So x = 4 is one of the answers.
.
Now set up a second equation using minus the quantity inside the absolute value signs. This
equation becomes:
.
-(3x + 2) = 14
.
The minus sign in front of the parentheses tells you to change the sign of every term in
the parentheses if you wish to remove the parentheses. Therefore, when you remove the
parentheses this equation becomes:
.
-3x - 2 = 14
.
Get rid of the -2 on the left side by adding 2 to both sides. When you do the equation
becomes:
.
-3x = 16
.
Now solve for x by dividing both sides by -3. This division makes the equation become:
.
x = -16/3
.
So now you have the two answers: x = 4 and x = -16/3
.
Let's check them out. The original equation was:
.

.
Setting x equal to 4 results in:
.

.
Multiplying inside the absolute value signs gives:
.

.
which simplifies to:
.

.
And since the absolute value of +14 is 14, this equation becomes:
.

.
which is true. Therefore, x = 4 is a good solution.
.
Next let's check out the other answer x = -16/3.
.
Begin with
.

.
Substitute -16/3 for x and the equation becomes:
.

.
Doing the multiplication inside the absolute value signs gives:
.

.
and since the equation simplifies to:
.

.
The addition inside the absolute value signs results in -14 so the equation becomes:
.

.
but the absolute value of -14 is 14, so the equation becomes:
.

.
and since this is true, the answer is also correct.
.
Hope this shows you a way to solve absolute value equations of this type. Just take the
plus and minus quantities of the expression inside the absolute value signs and set up
two equations. Then solve them just as you would an ordinary equation. This will give
you the answers. And it is a good practice to check your answers as was done above.
.

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