Question

Solve for x: 2|x - 3| + 1 = 7

Answer 1

2|x - 3| + 1 = 7
2|x - 3| = 6
|x - 3| = 3
Split: -(x-3)=3 ---> -x+3=3 ---> x=0
x-3=3 ---> x=6
Check your answers.
x=0,6

Answer 2

how does the x become a negative?

Answer 3

Absolute value means that anything in between the sign turns positive after whatever is inside is resolved. To find the x, we isolate everything until we have only the absolute value on one side and split it into two equations: one with -( stuff in absolute value )=whatever and ( stuff in absolute value )=whatever

Answer 4

Basically abs(x)=3 means that x can either be 3 or -3, we don't know, so we account for both situations.

Answer 5

The way i was taught was for example, for [x-3]=3 i would make another equation but with a negative answer like this [x-3]= -3

Answer 6

am i getting it correctly?

Answer 7

You can do that and it isn't wrong, but when you get to inequalities, you'll want to keep the negative on the side with the absolute value side so that you remember to flip the inequality side.
For equalities, it's a matter of preference, I guess, but a good habit for the future.