Question

3|x - 3| + 2 = 14

Answer 1

You need to get the absolute value alone on the left side and a number on the right side.
First, subtract 2 from both sides.
Then divide both sides by 3.
What do you have now?

Answer 2

3|x - 3| + 2 = 14
-2 -2
1|x - 3| + 2 = 12
/3 /3
0|x - 3| + 2 = 4
I dont think I did it correctly @mathstudent55

Answer 3

No, that's not it.
Follow along below where I explain step by step.

You subtract to undo an addition. You divide to undo a multiplication.

The first step is to subtract 2 from both sides to undo the +2 on the left side:
3|x - 3| + 2 = 14
-2 -2
----------------
3|x - 3| = 12

Now we see that the 3 is multiplying the absolute value, so we divide both sides by 3 to undo the multiplication by 3.

\( \dfrac{3|x - 3|}{3} = \dfrac{12}{3} \)

|x - 3| = 4

Now we have simply the absolute value of an expression equaling a number.

Answer 4

To solve an absolute value equation of the form |X| = b, wehre X is an expression in x and b is a number, you get rid of the absolute value symbol by changing the absolute value equation into the following two equations connected by the word "or."
X = b or X = -b

Here we have |x - 3| = 4, so to get rid of the absolute value symbols, we change into:
x - 3 = 4 or x - 3 = -4

Now we need to get rid of -3 on the left side. Since the 3 is being subtracted, we do the opposite operation. we add 3 to both sides of borth equations:

x - 3 = 4 or x - 3 = -4
+ 3 +3 + 3 +3
--------- ----------
x = 7 or x = -1

The final solution is: x = 7 or x = -1.