(x-4)/(2x+4) is greater than or equal to 1.

Question

How do i express solutions to inequalities in interval notation without using the calculator? please help.

(x-4)/(2x+4) >=1

multiplying by 2x+4

1) when (2x+4) is +,
x-4>=2x+4 or
x-2x>=8
-x>=8
x<=-8 notice the inequality reversed when multiplying by -1

2) when (2x-4) is -, you can work it out, but it should end up x>=-8

So the question then is when does 2x-4 become + or -
2x+4=0
x=-2 So for x<-2, 2x+4 is negative. looking at 1), we said the domain of the function was x<=-8 when 2x+4 was postive, but 2x+4 is postive when x>-2, so there is no x that can be <-8 and >-2, the solution does not exist.
Examining 2), x>=-8 for when 2x+4 is negative, but for 2x+4 to be negative, then x<-2. soe the range for x is between -8 and -2. Check Now, three values: x=-10; -5; 0 See if the inequality given works for -5 but not the other values of x.

2x+15>3

i need help on it , i really don't understand

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