Question

Solve the absolute equation
|2x+1| ≥ 9

Answer 1

I love absolute value equations!! :O
Since |2x +1| must be >= 9, we break it apart into 2 equations
For all values that 2x +1 < 0, we use -(2x+1)>= 9
For all values that 2x+1 >= 0, we use (2x +1) >=9

2x+1>0
2x>1
x>.5

For all values greater than .5, we use the values of 2x+1 >= 9, or x >= 5

For all values less than .5, we use the values of -(2x+1) >=9
Which becomes 2x+1 <= -9
Which becomes x<=-5

The final answer is -5>=x AND x>=5
\[(-\infty,-5] U [5, \infty)\]

Answer 2

first we make two equations from the first one give.

take the equation given and just remove the absolute value signs. this is one of the two equations we will use to solve.
so doing this, what do you get when you isolate x?

Answer 3

the solution posted above is incomplete, if you want further help just message me ^_^